Editing Electrical length (section)

=== 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" />