Editing Electrical length (section)

== Antennas ==
[[File:Dipole antenna standing waves animation 1-10fps.gif|thumb|upright=1.2|A half-wave [[dipole antenna]] showing the standing waves of voltage ''(red)'' and current ''(blue)'' on the antenna.  The antenna is resonant at the frequency at which the electrical length is approximately equal to <math>\lambda/2 = c/2f</math>]]

An important class of radio [[antenna (radio)|antenna]] is the ''thin element antenna'' in which the radiating elements are conductive wires or rods.  These include [[monopole antenna]]s and [[dipole antenna]]s, as well as antennas based on them such as the [[whip antenna]], [[T antenna]], [[mast radiator]], [[Yagi antenna|Yagi]], [[log periodic antenna|log periodic]], and [[turnstile antenna]]s.  These are [[resonant]] antennas, in which the radio frequency electric currents travel back and forth in the antenna conductors, reflecting from the ends.

If the antenna rods are not too thick (have a large enough length to diameter ratio), the current along them is close to a sine wave, so the concept of electrical length also applies to these.<ref name="Weik" />   The current is in the form of two oppositely directed sinusoidal traveling waves which reflect from the ends, which interfere to form [[standing wave]]s.   The electrical length of an antenna, like a transmission line, is its length in wavelengths of the current on the antenna at the operating frequency.<ref name="ATIS" /><ref name="Radioman3&2">{{cite book
 | title  = Radioman 3 & 2, US Navy Training Course NAVPERS 10228-E
 | publisher = Bureau of Naval Personnel, US Navy
 | date   = 1967
 | pages  = 131
 | url    = https://books.google.com/books?id=v1xjCRjU6pAC&dq=%22electrical+length%22&pg=PA131
 | doi    = 
 | id     = 
 | isbn   = 
 }}</ref><ref name="Singh">{{cite book
 | last1  = Singh
 | first1 = Yaduvir 
 | title  = Electro Magnetic Field Theory
 | publisher = Dorling Kindersley
 | date   = 2011
 | location = 
 | pages  = 451
 | url    = https://books.google.com/books?id=0-PfbT49tJMC&q=%22electrical+length%22&pg=PA451
 | doi    = 
 | id     = 
 | isbn   = 9788131760611
 }}</ref><ref name="Schmitt" />{{rp|p.91–104}}  An antenna's [[resonant frequency]], [[radiation pattern]], and driving point [[input impedance|impedance]] depend not on its physical length but on its electrical length.<ref name="Griffith">{{cite book
 | last1  = Griffith
 | first1 = B. Whitfield 
 | title  = Radio-electronic Transmission Fundamentals
 | publisher = Noble Publishing
 | series = 
 | volume = 
 | edition = 
 | date   = 2000
 | location = 
 | pages  = 335–337
 | language = 
 | url    = https://books.google.com/books?id=m5DIroWLw2EC&pg=PA335
 | doi    = 
 | id     = 
 | isbn   = 9781884932137
 }}</ref>  A thin antenna element is resonant at frequencies at which the standing current wave has a node (zero) at the ends (and in monopoles an [[antinode]] (maximum) at the ground plane).  A [[dipole antenna]] is resonant at frequencies at which its electrical length is a half wavelength (<math>\lambda/2, \phi = 180^\circ \;\text{or}\; \pi \;\text{radians}</math>)<ref name="Radioman3&2" /> or a multiple of it.    A [[monopole antenna]] is resonant at frequencies at which its electrical length is a quarter wavelength (<math>\lambda/4, \phi = 90^\circ \;\text{or}\; \pi/2 \;\text{radians}</math>) or a multiple of it.

Resonant frequency is important because at frequencies at which the antenna is [[resonant]] the input [[electrical impedance|impedance]] it presents to its feedline is purely [[electrical resistance|resistive]].  If the resistance of the antenna is matched to the [[characteristic impedance|characteristic resistance]] of the feedline, it absorbs all the power supplied to it, while at other frequencies it has [[Electrical reactance|reactance]] and reflects some power back down the line toward the transmitter, causing [[standing wave]]s (high [[standing wave ratio|SWR]]) on the feedline.  Since only a portion of the power is radiated this causes inefficiency, and can possibly overheat the line or transmitter.  Therefore, transmitting antennas are usually designed to be resonant at the transmitting frequency; and if they cannot be made the right length they are ''electrically lengthened'' or ''shortened'' to be resonant (see below).

=== End effects ===
[[File:DipoleReductionFactor.jpg|thumb|upright=1.6|Reduction factor of physical length of a resonant dipole from a half-wavelength electrical length as a function of element thickness]] 
A thin-element antenna can be thought of as a transmission line with the conductors separated,<ref name="AF52-19" />   so the near-field electric and magnetic fields extend further into space than in a transmission line, in which the fields are mainly confined to the vicinity of the conductors.  Near the ends of the antenna elements the electric field is not perpendicular to the conductor axis as in a transmission line but spreads out in a fan shape (fringing field).<ref name="Schelkunoff">{{cite book
 | last1  = Schelkunoff
 | first1 = Sergei A.
 | last2  = Friis
 | first2 = Harold T.
 | title  = Antennas: Theory and Practice
 | publisher = John Wiley and Sons
 | date   = 1952
 | pages  = 245
 | url    = https://archive.org/details/antennastheorypr00sche/page/n5/mode/2up
 | doi    = 
 | id     = 
 }}</ref>  As a result, the end sections of the antenna have increased capacitance, storing more charge, so the current waveform departs from a sine wave there, decreasing faster toward the ends.<ref name="Rudge">{{cite book
 | last1  = Rudge
 | first1 = Alan W.
 | last2  = Milne
 | first2 = K.
 | title  = The Handbook of Antenna Design, Vol. 2
 | publisher = IET
 | date   = 1982 
 | pages = 564
 | url    = https://books.google.com/books?id=QjYtNJZmWLEC&dq=%22umbrella+antenna%22&pg=PA588
 | isbn   = 9780906048870
 }}</ref>  When approximated as a sine wave, the current does not quite go to zero at the ends; the [[node (physics)|nodes]] of the current standing wave, instead of being at the ends of the element, occur somewhat beyond the ends.<ref>The effect of this on the antenna is equivalent to the current wave moving along the antenna at a phase velocity <math>v_\text{p}</math> lower than the speed of light <math>c</math>, as in a transmission line. Some sources explain it this way: {{cite book
 | last1  = Carr
 | first1 = Joseph
 | last2  = Hippisley
 | first2 = George
 | title  = Practical Antenna Handbook, 5th Ed.
 | publisher = McGraw-Hill
 | date   = 2012
 | pages  = 105
 | url    = http://hamradio.uz/media/uploads/2018/04/06/practical_antenna_handbook__2012.pdf
 | id     = 
 | isbn   = 9780071639590
 }} and {{cite book
 | last1  = Rudge
 | first1 = Alan W.
 | last2  = Milne
 | first2 = K.
 | title  = The Handbook of Antenna Design, Vol. 2
 | publisher = IET
 | date   = 1982 
 | pages  = 564
 | url    = https://books.google.com/books?id=QjYtNJZmWLEC&dq=%22umbrella+antenna%22&pg=PA588
 | isbn   = 9780906048870
 }}  However, this is a physically misleading description; the phase velocity is not constant along the element.</ref>  Thus the electrical length of the antenna is longer than its physical length.

The electrical length of an antenna element also depends on the length-to-diameter ratio of the conductor.<ref name="Lewis">{{cite book
 | last1  = Lewis
 | first1 = Geoff 
 | title  = Newnes Communications Technology Handbook
 | publisher = Elsevier
 | date   = 2013
 | pages  = 46
 | url    = https://books.google.com/books?id=_7z8BAAAQBAJ&q=%22electrical+length%22+%22velocity+factor%22
 | doi    = 
 | id     = 
 | isbn   =  9781483101026
 }}</ref><ref name="AF52-19">{{cite book
 | title  = US Air Force Manual 52-19: Antenna Systems
 | publisher = US Air Force
 | date   = 1953
 | pages  = 104–105
 | url    = https://books.google.com/books?id=bDC0pGpz5EQC&dq=%22length+to+diameter+ratio%22+%22electrical+length%22&pg=PA105
 | doi    = 
 | id     = 
 | isbn   = 
 }}</ref><ref name="ARRL">{{cite book
 | title  = The A.R.R.L. Antenna Book, 5th Ed.
 | publisher = American Radio Relay League
 | date   = 1949
 | pages  = 27–28
 | language = 
 | url    = https://books.google.com/books?id=2Y1RAAAAMAAJ&dq=%22electrical+length%22&pg=PA27
 | doi    = 
 | id     = 
 | isbn   = 
 }}</ref><ref name="Carr1">{{cite book
 | last1  = Carr
 | first1 = Joseph
 | title  = Antenna Toolkit, 2nd Ed.
 | publisher = Elsevier
 | date   = 2001
 | location = 
 | pages  = 52–54
 | language = 
 | url    = https://books.google.com/books?id=kEbQ3io1q6sC&dq=%22transmission+line%22+%22velocity+factor%22&pg=PA52
 | doi    = 
 | id     = 
 | isbn   =  9780080493886
 }}</ref>  As the ratio of the diameter to wavelength increases, the capacitance increases, so the node occurs farther beyond the end, and the electrical length of the element increases.<ref name="Lewis" /><ref name="ARRL" />  When the elements get too thick, the current waveform becomes significantly different from a sine wave, so the entire concept of electrical length is no longer applicable, and the behavior of the antenna must be calculated by [[electromagnetic simulation]] computer programs like [[Numerical Electromagnetics Code|NEC]].

As with a transmission line, an antenna's electrical length is increased by anything that adds shunt capacitance or series inductance to it, such as the presence of high permittivity dielectric material around it.  In [[microstrip antenna]]s which are fabricated as metal strips on [[printed circuit board]]s, the [[dielectric constant]] of the substrate board increases the electrical length of the antenna.  Proximity to the Earth or a [[ground plane]], a dielectric coating on the conductor, nearby grounded towers, metal structural members, [[guy line]]s and the capacitance of insulators supporting the antenna also increase the electrical length.<ref name="ARRL" />

These factors, called "end effects", cause the electrical length of an antenna element to be somewhat longer than the length of the same wave in free space.  In other words, the physical length of the antenna at resonance will be somewhat shorter than the resonant length in free space (one-half wavelength for a dipole, one-quarter wavelength for a monopole).<ref name="Lewis" /><ref name="ARRL" />  As a rough generalization, for a typical [[dipole antenna]], the physical resonant length is about 5% shorter than the free space resonant length.<ref name="Lewis" /><ref name="ARRL" />

=== Electrical lengthening and shortening ===
In many circumstances for practical reasons it is inconvenient or impossible to use an antenna of resonant length.  An antenna of nonresonant length at the operating frequency can be made resonant by adding a [[electrical reactance|reactance]], a [[capacitance]] or [[inductance]], either in the antenna itself or in a [[matching network]] between the antenna and its [[feedline]].<ref name="ARRL" />  A nonresonant antenna appears at its feedpoint electrically equivalent to a [[electrical resistance|resistance]] in series with a reactance.  Adding an equal but opposite type of reactance in series with the feedline will cancel the antenna's reactance; the combination of the antenna and reactance will act as a series [[resonant circuit]], so at its operating frequency its input impedance will be purely resistive, allowing it to be fed power efficiently at a low [[standing wave ratio|SWR]] without reflections.

In a common application, an antenna which is ''electrically short'', shorter than its fundamental resonant length, a monopole antenna with an electrical length shorter than a quarter-wavelength (<math>\lambda/4</math>), or a dipole antenna shorter than a half-wavelength (<math>\lambda/2</math>) will have [[capacitive reactance]].  Adding an [[inductor]] (coil of wire), called a [[loading coil]], at the feedpoint in series with the antenna, with [[inductive reactance]] equal to the antenna's capacitive reactance at the operating frequency, will cancel the capacitance of the antenna, so the combination of the antenna and coil will be resonant at the operating frequency.  Since adding inductance is equivalent to increasing the electrical length, this technique is called '''electrically lengthening''' the antenna.  This is the usual technique for matching an electrically short transmitting antenna to its feedline, so it can be fed power efficiently.  However, an electrically short antenna that has been loaded in this way still has the same [[radiation pattern]]; it does not radiate as much power, and therefore has lower [[antenna gain|gain]] than a full-sized antenna.

Conversely, an antenna longer than resonant length at its operating frequency, such as a monopole longer than a quarter wavelength but shorter than a half wavelength, will have [[inductive reactance]]. This can be cancelled by adding a [[capacitor]] of equal but opposite reactance at the feed point to make the antenna resonant.  This is called '''electrically shortening''' the antenna.

=== Scaling properties of antennas ===
Two antennas that are [[similarity (geometry)|similar]] (scaled copies of each other), fed with different frequencies, will have the same [[radiation resistance]] and [[radiation pattern]] and fed with equal power will radiate the same power density in any direction if they have the same electrical length at the operating frequency; that is, if their lengths are in the same proportion as the wavelengths.<ref name="Levin">{{cite book
 | last1  = Levin
 | first1 = Boris 
 | title  = Wide-Range Antennas
 | publisher = CRC Press
 | date   = 2019
 | pages  = 26 
 | url    = https://books.google.com/books?id=fn-JDwAAQBAJ&dq=antenna+scaling&pg=SA9-PA26
 | doi    = 
 | id     = 
 | isbn   = 9781351043229
 }}</ref><ref name="Schmitt" />{{rp|p.12–14}}
:<math>{l_\text{1} \over l_\text{2}} = {\lambda_\text{1} \over \lambda_\text{2}} = {f_\text{2} \over f_\text{1}}</math>
This means the length of antenna required for a given [[antenna gain]] scales with the wavelength (inversely with the frequency), or equivalently the [[antenna aperture|aperture]] scales with the square of the wavelength.

=== Electrically short antennas ===
An electrically short conductor, much shorter than one wavelength, makes an inefficient radiator of [[electromagnetic wave]]s.  As the length of an antenna is made shorter than its fundamental resonant length (a half-wavelength for a dipole antenna and a quarter-wavelength for a monopole), the [[radiation resistance]] the antenna presents to the feedline decreases with the square of the electrical length, that is the ratio of physical length to wavelength, <math>(l/\lambda)^2</math>.    As a result, other resistances in the antenna, the ohmic resistance of metal antenna elements, the ground system if present, and the loading coil, dissipate an increasing fraction of transmitter power as heat.  A monopole antenna with an electrical length below  .05<math>\lambda</math> or 18° has a radiation resistance of less than one ohm, making it very hard to drive.

A second disadvantage is that since the capacitive reactance of the antenna and inductive reactance of the required loading coil do not decrease,  the [[Q factor]] of the antenna increases; it acts electrically like a high Q [[tuned circuit]].  As a result, the [[bandwidth (signal processing)|bandwidth]] of the antenna decreases with the square of electrical length, reducing the [[data rate]] that can be transmitted.  At [[very low frequency|VLF]] frequencies even the huge toploaded wire antennas that must be used have  bandwidths of only ~10 hertz, limiting the [[data rate]] that can be transmitted.