View source for Engineering:Twin-lead

{{Short description|Two-conductor flat cable used to carry radio frequency signals}}
[[File:Twinlead.gif|thumb|300 ohm twin-lead]]
{{Antennas|components}}
'''Twin-lead''' cable is a [[Physics:Electrical conductor|two-conductor]] flat cable used as a [[Engineering:Balanced line|balanced transmission line]] to carry [[Engineering:Radio frequency|radio frequency]] (RF) signals.  It is constructed of two stranded or solid [[Chemistry:Copper|copper]] or copper-clad steel wires, held a precise distance apart by a plastic (usually [[Chemistry:Polyethylene|polyethylene]]) ribbon.  The uniform spacing of the wires is the key to the cable's function as a transmission line; any abrupt changes in spacing would reflect some of the signal back toward the source. The plastic also covers and insulates the wires.  It is available with several different values of [[Physics:Characteristic impedance|characteristic impedance]], the most common type is 300 ohm.

Twin lead is mainly used as an antenna feedline at shortwave and [[Engineering:Very high frequency|VHF]] frequencies, to connect [[Engineering:Radio receiver|radio receiver]]s and [[Engineering:Transmitter|transmitter]]s to their [[Engineering:Antenna (radio)|antenna]]s.  It can have significantly lower signal loss than miniature flexible [[Engineering:Coaxial cable|coaxial cable]], the main alternative type of feedline at these frequencies;  for example, type RG-58 coaxial cable loses 6.6&nbsp;dB per {{convert|100|m}} at 30&nbsp;MHz, while 300&nbsp;ohm twin-lead loses only 0.55&nbsp;dB.<ref>{{cite web |url=http://www.zs6hvb.za.net/index.php/our-favourite-links/why-ladder-line |title=Why ladder line? |website=Highveld Amateur Radio Club}}</ref>  300 ohm twin lead is widely used to connect FM radios to their antennas, and was previously used to connect [[Engineering:Television antenna|television antenna]]s to [[Engineering:Television|television]]s until it was replaced by coaxial cable.  However, it is more vulnerable to interference; proximity to metal objects will inject signals into twin-lead that would be blocked out by coaxial cable.  It therefore requires spacing around [[Engineering:Rain gutter|rain gutter]]s, and standoff insulators along metal support masts.

==Characteristics and uses==
Twin lead and other types of parallel-conductor transmission line are mainly used to connect radio transmitters and [[Engineering:Radio receiver|receivers]] to their [[Engineering:Antenna (radio)|antenna]]s. Parallel transmission line has the advantage that its losses per unit length are an order of magnitude smaller than that of [[Engineering:Coaxial cable|coaxial cable]], the main alternative form of transmission line. Its disadvantages are that it is more vulnerable to interference, and must be kept away from metal objects which can cause power losses. For this reason, when installed along the outside of buildings and on antenna masts, standoff insulators must be used. It is also common practice to twist the twin lead on long free standing lengths to further reject any induced imbalances to the line.

Twin-lead is supplied in several different sizes, with values of 600, 450, 300, and 75&nbsp;[[Ohm|ohm]] [[Physics:Characteristic impedance|characteristic impedance]]. The most common, 300&nbsp;ohm twin-lead, was once widely used to connect [[Engineering:Television|television]] sets and FM radios to their receiving antennas. 300&nbsp;ohm twin-lead for television installations has been largely replaced with 75&nbsp;ohm [[Engineering:Coaxial cable|coaxial cable]] feedlines. Twin-lead is also used in amateur radio stations as a [[Engineering:Transmission line|transmission line]] for [[Engineering:Balanced line|balanced]] transmission of [[Engineering:Radio frequency|radio frequency]] signals.

The characteristic [[Physics:Electrical impedance|impedance]] of twin-lead is a function of the wire diameter and its spacing; in 300&nbsp;ohm twin-lead, the most common type, the wire is usually 20 or 22&nbsp;gauge (0.52 or 0.33&nbsp;mm{{sup|2}}), about 7.5&nbsp;mm (0.30&nbsp;inches) apart.<ref name="ARRL2">{{cite book   
  | last = Straw
  | first = R. Dean, Ed.
  | title = The ARRL Antenna Book, 19th Ed.
  | publisher = American Radio Relay League
  | year = 2000
  | location = USA
  | pages = 24.16–17
  | url = 
  | doi = 
  | id = 
  | isbn = 0-87259-817-9}}</ref> This is well matched with the natural impedance of a folded dipole antenna, which is normally around 275&nbsp;ohms. Twin-lead generally has higher impedance than the other common transmission wiring, [[Engineering:Coaxial cable|coaxial cable]] (coax). The widely used [[Engineering:RG-6|RG-6]] coax has a characteristic impedance of 75&nbsp;ohms, which requires the use of a [[Engineering:Balun|balun]] to match impedance when used with common antenna types.

==How it works==
[[File:Tvbalun.jpg|thumb|left|A 300-to-75-ohm balun, showing twin-lead on the right hand side]]

Twin lead is a form of parallel-wire [[Engineering:Balanced line|balanced transmission line]].  The separation between the two wires in twin-lead is small compared to the [[Wavelength|wavelength]] of the [[Engineering:Radio frequency|radio frequency]] (RF) signal carried on the wire.<ref name="ARRL">{{cite book   
  | last = Straw
  | first = R. Dean, Ed.
  | title = The ARRL Antenna Book, 19th Ed.
  | publisher = American Radio Relay League
  | year = 2000
  | location = USA
  | pages = 24.1
  | url = 
  | doi = 
  | id = 
  | isbn = 0-87259-817-9}}</ref>  The RF [[Physics:Electric current|current]] in one wire is equal in magnitude and opposite in direction to the RF current in the other wire.  Therefore, in the far field region far from the transmission line, the [[Radio wave|radio wave]]s radiated by one wire are equal in magnitude but opposite in phase (180° [[Physics:Out of phase|out of phase]]) to the waves radiated by the other wire, so they [[Superposition principle|superpose]] and cancel each other.<ref name="ARRL" />  The result is that almost no net radio energy is radiated by the line.

Similarly, any interfering external radio waves will induce equal, in phase RF currents, traveling in the same direction, in the two wires.  Since the load at the destination end is connected ''across'' the wires, only ''differential'', oppositely-directed currents in the wires create a current in the load.   Thus the interfering currents are canceled out, so twin lead does not tend to pick up radio noise.

However, if a piece of metal is located sufficiently close to a twin-lead line, within a distance comparable to the wire spacing, it will be significantly closer to one wire than the other.  As a result, the RF current induced in the metal object by one wire will be greater than the opposing current induced by the other wire, so the currents will no longer cancel.  Thus nearby metal objects can cause power losses in twin lead lines, through energy dissipated as heat by induced currents.  Similarly, radio noise originating in cables or metal objects located near the twin-lead line can induce unbalanced currents in the wires, coupling noise into the line.   Therefore, the line must be kept at a distance from metal objects such as gutters and masts.

In order to prevent power from being reflected from the load end of the line, causing high [[Engineering:Standing wave ratio|SWR]] and inefficiency, the load must have an [[Physics:Electrical impedance|impedance]] which matches the [[Physics:Characteristic impedance|characteristic impedance]] of the line.  This causes the load to appear electrically identical to a continuation of the line, preventing reflections.   Similarly, to transfer power efficiently into the line, the source must also match the characteristic impedance.  To connect a balanced transmission line to an unbalanced line like [[Engineering:Coaxial cable|coaxial cable]], a device called a [[Engineering:Balun|balun]] must be used.

==<span class="anchor" id="Ladder_line">Ladder line</span>==
{{multiple image
 | caption_align=center | header_align=center | align = right | total_width = 440
 | image1 = Electronics Technician - Volume 7 - Figure 3-10.jpg
 | width1 = 750 | height2 = 536
 | alt1 = Nominal 300Ω
 | caption1 = 300&nbsp;Ω twin lead or two wire ribbon cable. Note the plastic between the wires is unbroken – no "windows". 
 | image2 = Ladder line.jpg
 | width2 = 750 | height1 = 536
 | alt2 = Nominal 450Ω line
 | caption2 = Nominal 450&nbsp;ohm "window line". The opening cut between the wires is one of the "windows".
}}
Parallel wire line comes in three distinct forms:
* '''twin lead''', or (two wire) ''ribbon cable'',<br/>discussed in the section above
* '''window line'''
* '''ladder line''' or ''open wire line''

'''Window line''' is a variation of twin lead which is constructed similarly, except that the polyethylene webbing between the wires which holds them apart has rectangular openings ("windows") cut in it.<ref name=ARRL2/><ref name=QST2>{{cite journal |last=Ford |first=Steve |date=December 1993 |title=The Lure Of Ladder Line |journal=QST |publisher=ARRL |url=http://www.w6ier.org/images/The%20Lure%20of%20Ladder%20Line.pdf |access-date=September 16, 2011 |archive-url=https://web.archive.org/web/20120402124811/http://www.w6ier.org/images/The%20Lure%20of%20Ladder%20Line.pdf |archive-date=2 April 2012 |url-status=dead}}</ref> Among the advantages to cutting "windows" in the ribbon is that the manufacturer can adjust the size of the cuts to make fine adjustments to the feedline's electrical properties. The windows lighten the line, and reduce the amount of surface on which dirt and moisture can accumulate, making window line somewhat less vulnerable to weather-induced changes in its characteristic impedance.<ref name=ARRL2/> The most common type is nominal 450&nbsp;Ω window line, which has a conductor spacing of about an inch ({{convert|1|in|disp=out}}); its actual impedance may be closer to 400&nbsp;Ω.<ref name=ARRL2/> It is also made in nominal 350&nbsp;Ω impedance. 
{{multiple image
 | caption_align=center |header_align=center | align = right | total_width = 440 | mode=packed
 | image1 = Ladder line.png
 | width1 = 750 | height1 = 536
 | alt1 = Nominal 600Ω line sketch
 | caption1 = 500–600&nbsp;Ω "ladder line", or "open wire line". The insulating spacers between the wires are the "rungs" of the ladder.
 | image2 = LadderlineW3NP.JPG
 | width2 = 750 | height2 = 536
 | alt2 = Nominal 600Ω overhead
 | caption2 = 500–600&nbsp;Ω "open wire line" or "ladder line" feeding a high wire antenna
}}

'''Ladder line''' is an older, simpler form of parallel-wire line, often called ''open wire line'', that can either be commercially manufactured or DIY-made (construction is easy, though tedious, and originally all radio amateurs made their own open wire line). It consists of two wires (usually either clad in a DC [[Physics:Insulator (electricity)|insulator]] or coated with a [[Chemistry:List of polyurethane applications#electronic components anchor|durable lacquer]]) with "rungs" of insulating plastic (formerly treated wood or ceramic) holding the wires at some constant spacing, about two to {{convert|5|in|cm|spell=in}} apart, with a rung about every {{convert|5|to(-)|12|in|cm|spell=in}}. Uniform wire spacing is important, but erratic distances between rung insulators don't matter. The configuration looks like a rope ladder, hence the name.

The ratio of chosen wire spacing to wire diameter determines the line's [[Physics:Characteristic impedance#|characteristic impedance]] – usually 500~600&nbsp;Ω. It also depends on the wire insulation's [[Chemistry:Relative permittivity|relative permittivity]] and conductive loss in the rung insulators, if significant.<ref name=qst>{{cite magazine |last=Danzer |first=Paul |date=April 2004 |title=Open wire feed line — a second look |magazine=QST Magazine |place=Newington, CT |publisher=American Radio Relay League |url=http://www.cqham.ru/forum/attachment.php?attachmentid=35851&d=1244391020 |access-date=16 September 2011}}</ref> For 500&nbsp;Ω line, two bare wires would be spaced 32× the wire diameter apart; about {{convert|4|in|cm|spell=in}}, for wire diameter {{convert|1/8|in|mm|sigfig=1}}. For 600&nbsp;Ω the same wire would be spaced {{convert|9|in|cm|spell=in}}.

==Impedance matching==
{{Main|Impedance matching}}
As a transmission line, transmission efficiency will be maximum when the [[Physics:Electrical impedance|impedance]] of the antenna, the characteristic impedance of the twin-lead line and the impedance of the equipment are the same. For this reason, when attaching a twin-lead line to a coaxial cable connection, such as the 300&nbsp;ohm twin-lead from a domestic television antenna to the television's 75&nbsp;ohm coax antenna input, a [[Engineering:Balun|balun]] with a 4:1 ratio<!-- Not 2:1 - Baluns are normally described by their impedance ratio, not the turns/voltage ratio --> is commonly used. Its purpose is double: first, it transforms twin-lead's 300&nbsp;ohm impedance to match the 75&nbsp;ohm coaxial cable impedance; and second, it transforms the balanced, symmetric transmission line to the unbalanced coax input. In general, when used as a feedline, twin-lead (especially ladder line versions) has a higher efficiency than coaxial cable when there is an impedance mismatch between the feedline and the source (or sink). For receive-only use this merely implies that the system can communicate under slightly less optimal conditions; for transmit use, this can often result in significantly less energy lost as heat in the transmission line.

Twin-lead also can serve as a convenient material with which to build a simple [[Physics:Dipole antenna#Folded dipole|folded dipole]] antenna. Such antennas may be fed either by using a 300&nbsp;ohm twin-lead feeder or by using a 300-to-75-ohm balun and using coaxial feedline and will usually handle moderate power loads without overheating.

==Characteristic impedance==
The characteristic impedance of a parallel-wire transmission line like twin lead or ladder line depends on its dimensions; the diameter of the wires {{mvar| d }} and their separation {{mvar| D }}. This is derived below.

The characteristic impedance  {{mvar|Z}}{{sub|o}}  of any transmission line is given by

:<math> Z_\mathsf{o} = \sqrt{ \frac{R + j\ \omega\ L }{\; G + j\ \omega\ C\;}\ }</math>

where for twin-lead line the [[Engineering:Primary line constants|primary line constants]] are

:<math>R = \frac{\ 2\ R_\mathsf{s}\ }{ \pi\ d }</math>

:<math>L = \frac{\mu}{\ \pi\ }\ \operatorname{arcosh} \left( \frac{\ D\ }{d} \right) </math>

:<math>G = \frac{ \pi\ \sigma }{\ \operatorname{arcosh} \left( \frac{\ D\ }{d} \right)\ } </math>

:<math>C = {{\pi\ \varepsilon l}\over{\ \operatorname{arcosh} \left( \frac{\ D\ }{d} \right)\ }}</math>

where {{mvar| d }} is the wire diameter and {{mvar| D }} is the separation of the wires measured between their centre-lines, {{mvar| &epsilon; }} is the [[Physics:Permittivity|absolute permittivity]] between the wires, {{mvar| l }} is the length of the wire, and where the surface resistance of the wires is given by

:<math> R_\mathsf{s} = \sqrt{ \frac{\ \pi\ f\ \mu_\mathsf{c}\ }{ \sigma_\mathsf{c} } \; } ~.</math>

Neglecting the wire resistance {{mvar| R }} and the leakage conductance {{mvar| G }}, this gives

:<math> Z_\mathsf{o} = \frac{ \zeta_\mathsf{o} }{\ \pi \sqrt{\varepsilon_\mathsf{R}\ }\ }\ \operatorname{arcosh}\left( \frac{\ D\ }{d} \right) =  \frac{ \zeta_\mathsf{o} }{\ \pi \sqrt{\varepsilon_\mathsf{R}\ }\ }\ \ln\Biggl[\ \tfrac{\ D\ }{d} + \sqrt{ \left( \tfrac{\ D\ }{d} \right)^2 - 1 ~}\ \Biggr] ~.</math><ref>
{{cite book
 |last=Stewart |first=Wes, N7WS 
 |section=Balanced transmission line in current amateur practice
 |title=ARRL Antenna Compendium
 |volume=6
 |publisher=American Radio Relay League
 |location=Newington, CT
}}
</ref>
:<math> \quad = \frac{ \zeta_\mathsf{o} }{\ \pi \sqrt{\varepsilon_\mathsf{R}\ }\ } \left[ \ln\left(\frac{\ 2\ D\ }{d} \right) - \left( \frac{d}{\ 2\ D\ } \right)^2 - \operatorname{\mathcal{O}} \left\{\left( \tfrac{d}{\ 2\ D\ } \right)^4 \right\} \right] </math>
:<math> \quad  \approx \frac{\ 119.92\ \mathsf\Omega\ }{ \sqrt{\varepsilon_\mathsf{R}\ } } \left[ \ln \left( \frac{\ 2\ D\ }{d} \right) - \left( \frac{d}{\, 2\,D\,} \right)^2 \right] \approx \frac{\ 119.92\ \mathsf\Omega\ }{ \sqrt{ \varepsilon_\mathsf{R}\ } }\ \ln\left(\frac{\ 2\ D\ }{d} \right) ~.</math>

where {{mvar| &zeta;}}{{sub|o}}  is the [[Physics:Impedance of free space|impedance of free space]] (approximately 376.74&nbsp;Ω), {{mvar| ε}}{{sub|{{sc|r}}}}  is the [[Chemistry:Relative permittivity|relative permittivity]] (which for air is {{math|1.00054}}).

When the separation {{mvar| D }} is many times greater than the wire diameter {{mvar| d }} then the  {{math| arcosh }} function can be approximately replaced by a [[Natural logarithm|natural logarithm]] (with its argument doubled):

:<math>Z_\mathsf{o} = \frac{ 119.92\ \mathsf{\Omega} }{\ \sqrt{\varepsilon_\mathsf{R}\ }\ }\ \operatorname{arcosh}\left( \frac{\ D\ }{d} \right) \approx \frac{\ 119.92\ \mathsf{\Omega}\ }{\ \sqrt{ \varepsilon_\mathsf{R}\ }\ }\  \ln \left( \frac{\,2\,D\,}{d} \right) \approx \frac{\ 276\ \mathsf\Omega\ }{\sqrt{ \varepsilon_\mathsf{R}\ } }\  \log_{10} \left( \frac{\ 2\ D\ }{d} \right) ~.</math><ref>
{{cite book
 |title=ARRL Handbook for Amateur Radio
 |year=2000
 |page=19.3
 |publisher=American Radio Relay League
 |location=Newington, CT
}}
</ref>

The separation needed to achieve a given characteristic impedance <math>\ Z_\mathsf{o}\ </math> through two wires is therefore
:<math>D \approx d\ \cosh \left( \frac{\ \pi\ Z_\mathsf{o} \sqrt{\varepsilon_\mathsf{R}\ }\ }{ \zeta_\mathsf{o} } \right) ~.</math>

The dielectric material between the two conductors with either twin-lead or ladder line is not all air. The effect of a "mixed" dielectric, part air and part polyethylene or other plastic, is that the actual impedance will fall somewhere between the value calculated assuming all air or all polyethylene. Published, carefully measured values for {{mvar|Z}}{{sub|o}} will typically be more accurate than estimates from formulas.

==Antennas==
Twin-lead can be connected directly to a suitably designed antenna:

; [[Engineering:Shortwave broadband antenna#Windom anchor|Windom antenna]]: A multiply-resonant antenna whose resonant impedances cluster around {{val|300|u=Ω}}.
; [[Physics:Dipole antenna#Folded dipole|Folded dipole]]: Double-wire dipole whose characteristic impedance in free space is around {{val|300|u=Ω}}.
; [[Physics:Dipole antenna|Dipole]]: Although the center impedance at resonance is approximately {{val|73|u=Ω}} in [[Physics:Free space|free space]], in actual use it varies between {{val|30|and|100|u=Ω}}, depending on height above ground, so with high-impedance feedline a T-match or Y-match feed will probably be necessary.
; [[Engineering:Yagi–Uda antenna|Yagi–Uda antenna]]: Yagi and the simpler [[Engineering:Moxon antenna|Moxon antenna]], and other [[Physics:Directional antenna|directional antenna]]s; some special impedance matching arrangement at the feedpoint is necessary for any cabling, since interference between the typically close-spacing of the parallel near-resonant antenna segments causes low feedpoint resistance as well as making the antenna more directional.


==References==
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{{Reflist|25em}}

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{{DEFAULTSORT:Twin-Lead}}
[[Category:Antennas (radio)]]

{{Sourceattribution|Twin-lead}}