Coaxial cable From Wikipedia - Coaxial Characteristic Impedance Derivation

Coaxial Characteristic Impedance Derivation[edit]

Coaxial Cable Dimensions. D is the radius of the larger conductor and d is the radius of the smaller conductor.

Taking the characteristic impedance at high frequencies,

{\displaystyle Z_{0}={\sqrt {\frac {L}{C}}}}

One should also know the inductance and capacitance of the two concentric cylindrical conductors which is the coaxial cable. By definition {\displaystyle C=Q/V} and getting the electric field by the formula of electric field of an infinite line,

{\displaystyle {\vec {E}}={\frac {Q}{2\pi \epsilon _{o}}}{\frac {\hat {r}}{r}}}^[16]

where {\displaystyle Q} is charge,{\displaystyle \epsilon _{o}} is the permittivity of free space, {\displaystyle r} is the radial distance and {\displaystyle {\hat {r}}} is the unit vector in the direction away from the axis. The Voltage, V, is

{\displaystyle V=Ed=-\int _{d}^{D}{\frac {Q}{2\pi \epsilon _{o}r}}dr={\frac {Q}{2\pi \epsilon _{o}}}ln{\frac {D}{d}}}

where {\displaystyle D} is the diameter of the bigger conductor and {\displaystyle d} is the diameter of the smaller conductor. The capacitance can then be solved by substitution,

{\displaystyle C={\frac {Q}{V}}={\frac {2\pi \epsilon _{o}}{ln{\frac {D}{d}}}}}

and the inductance is taken from Ampere's Law for two concentric conductors (coaxial wire) and with the definition of inductance,

{\displaystyle B={\frac {\mu _{o}I}{2\pi r}}}^[17] and {\displaystyle L={\frac {\phi }{I}}=\int {\frac {B}{I}}dS}

where {\displaystyle B} is magnetic induction, {\displaystyle \mu _{o}} is the permeability of free space, {\displaystyle \phi } is the magnetic flux and {\displaystyle dS} is the differential surface. Taking the inductance per meter,

{\displaystyle L=\int \limits _{d}^{D}{\frac {\mu _{o}}{2\pi r}}dr={\frac {\mu _{o}}{2\pi }}ln{\frac {D}{d}}},^[18]

Substituting the derived capacitance and inductance,

{\displaystyle Z_{0}={\sqrt {\frac {L}{C}}}={\frac {1}{2\pi }}{\sqrt {\frac {\mu }{\epsilon }}}\ln {\frac {D}{d}}}^[11]

Issues[edit]

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Signal leakage[edit]

Signal leakage is the passage of electromagnetic fields through the shield of a cable and occurs in both directions. Ingress is the passage of an outside signal into the cable and can result in noise and disruption of the desired signal. Egress is the passage of signal intended to remain within the cable into the outside world and can result in a weaker signal at the end of the cable and radio frequency interference to nearby devices. Severe leakage usually results from improperly installed connectors or faults in the cable shield.

For example, in the United States, signal leakage from cable television systems is regulated by the FCC, since cable signals use the same frequencies as aeronautical and radionavigation bands. CATV operators may also choose to monitor their networks for leakage to prevent ingress. Outside signals entering the cable can cause unwanted noise and picture ghosting. Excessive noise can overwhelm the signal, making it useless.

An ideal shield would be a perfect conductor with no holes, gaps, or bumps connected to a perfect ground. However, a smooth solid highly conductive shield would be heavy, inflexible, and expensive. Such coax is used for straight line feeds to commercial radio broadcast towers. More economical cables must make compromises between shield efficacy, flexibility, and cost, such as the corrugated surface of flexible hardline, flexible braid, or foil shields. Since shields cannot be perfect conductors, current flowing on the inside of the shield produces an electromagnetic field on the outer surface of the shield.

Consider the skin effect. The magnitude of an alternating current in a conductor decays exponentially with distance beneath the surface, with the depth of penetration being proportional to the square root of the resistivity. This means that, in a shield of finite thickness, some small amount of current will still be flowing on the opposite surface of the conductor. With a perfect conductor (i.e., zero resistivity), all of the current would flow at the surface, with no penetration into and through the conductor. Real cables have a shield made of an imperfect, although usually very good, conductor, so there must always be some leakage.

The gaps or holes, allow some of the electromagnetic field to penetrate to the other side. For example, braided shields have many small gaps. The gaps are smaller when using a foil (solid metal) shield, but there is still a seam running the length of the cable. Foil becomes increasingly rigid with increasing thickness, so a thin foil layer is often surrounded by a layer of braided metal, which offers greater flexibility for a given cross-section.

Signal leakage can be severe if there is poor contact at the interface to connectors at either end of the cable or if there is a break in the shield.

To greatly reduce signal leakage into or out of the cable, by a factor of 1000, or even 10,000, superscreened cables are often used in critical applications, such as for neutron flux counters in nuclear reactors.

Superscreened cables for nuclear use are defined in IEC 96-4-1, 1990, however as there have been long gaps in the construction of nuclear power stations in Europe, many existing installations are using superscreened cables to the UK standard AESS(TRG) 71181^[19]which is referenced in IEC 61917.^[20]

Ground loops[edit]

A continuous current, even if small, along the imperfect shield of a coaxial cable can cause visible or audible interference. In CATV systems distributing analog signals the potential difference between the coaxial network and the electrical grounding system of a house can cause a visible "hum bar" in the picture. This appears as a wide horizontal distortion bar in the picture that scrolls slowly upward. Such differences in potential can be reduced by proper bonding to a common ground at the house. See ground loop.

Noise[edit]

External fields create a voltage across the inductance of the outside of the outer conductor between sender and receiver. The effect is less when there are several parallel cables, as this reduces the inductance and, therefore, the voltage. Because the outer conductor carries the reference potential for the signal on the inner conductor, the receiving circuit measures the wrong voltage.

Transformer effect[edit]

The transformer effect is sometimes used to mitigate the effect of currents induced in the shield. The inner and outer conductors form the primary and secondary winding of the transformer, and the effect is enhanced in some high-quality cables that have an outer layer of mu-metal. Because of this 1:1 transformer, the aforementioned voltage across the outer conductor is transformed onto the inner conductor so that the two voltages can be cancelled by the receiver. Many sender and receivers have means to reduce the leakage even further. They increase the transformer effect by passing the whole cable through a ferrite core one or more times.

Common mode current and radiation[edit]

Common mode current occurs when stray currents in the shield flow in the same direction as the current in the center conductor, causing the coax to radiate.

Most of the shield effect in coax results from opposing currents in the center conductor and shield creating opposite magnetic fields that cancel, and thus do not radiate. The same effect helps ladder line. However, ladder line is extremely sensitive to surrounding metal objects, which can enter the fields before they completely cancel. Coax does not have this problem, since the field is enclosed in the shield. However, it is still possible for a field to form between the shield and other connected objects, such as the antenna the coax feeds. The current formed by the field between the antenna and the coax shield would flow in the same direction as the current in the center conductor, and thus not be canceled. Energy would radiate from the coax itself, affecting the radiation pattern of the antenna. With sufficient power this could be a hazard to people near the cable. A properly placed and properly sized balun can prevent common mode radiation in coax. An isolating transformer or blocking capacitor can be used to couple a coaxial cable to equipment, where it is desirable to pass radio-frequency signals but to block direct current or low-frequency power.

Standards[edit]

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Most coaxial cables have a characteristic impedance of either 50, 52, 75, or 93 Ω. The RF industry uses standard type-names for coaxial cables. Thanks to television, RG-6 is the most commonly used coaxial cable for home use, and the majority of connections outside Europe are by F connectors.

A series of standard types of coaxial cable were specified for military uses, in the form "RG-#" or "RG-#/U". They date from World War II and were listed in MIL-HDBK-216 published in 1962. These designations are now obsolete. The RG designation stands for Radio Guide; the U designation stands for Universal. The current military standard is MIL-SPEC MIL-C-17. MIL-C-17 numbers, such as "M17/75-RG214", are given for military cables and manufacturer's catalog numbers for civilian applications. However, the RG-series designations were so common for generations that they are still used, although critical users should be aware that since the handbook is withdrawn there is no standard to guarantee the electrical and physical characteristics of a cable described as "RG-# type". The RG designators are mostly used to identify compatible connectors that fit the inner conductor, dielectric, and jacket dimensions of the old RG-series cables.

Dielectric material codes

• FPE is foamed polyethylene

• PE is solid polyethylene

• PF is polyethylene foam

• PTFE is polytetrafluoroethylene;

• ASP is air space polyethylene^[42]

VF is the Velocity Factor; it is determined by the effective {\displaystyle \epsilon _{r}} and {\displaystyle \mu _{r}}^[43]

• VF for solid PE is about 0.66

• VF for foam PE is about 0.78 to 0.88

• VF for air is about 1.00

• VF for solid PTFE is about 0.70

• VF for foam PTFE is about 0.84

There are also other designation schemes for coaxial cables such as the URM, CT, BT, RA, PSF and WF series.

RG-6 Coaxial cable

RG-142 Coaxial cable

RG-405 semi-rigid coaxial cable

High-end coaxial audio cable (S/PDIF)

Uses[edit]

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Short coaxial cables are commonly used to connect home video equipment, in ham radio setups, and in measurement electronics. While formerly common for implementing computer networks, in particular Ethernet ("thick" 10BASE5and "thin" 10BASE2), twisted pair cables have replaced them in most applications except in the growing consumer cable modem market for broadband Internet access.

Long distance coaxial cable was used in the 20th century to connect radio networks, television networks, and Long Distance telephone networks though this has largely been superseded by later methods (fibre optics, T1/E1, satellite).

Shorter coaxials still carry cable television signals to the majority of television receivers, and this purpose consumes the majority of coaxial cable production. In 1980s and early 1990s coaxial cable was also used in computer networking, most prominently in Ethernet networks, where it was later in late 1990s to early 2000s replaced by UTP cables in North America and STP cables in Western Europe, both with 8P8C modular connectors.

Micro coaxial cables are used in a range of consumer devices, military equipment, and also in ultra-sound scanning equipment.

The most common impedances that are widely used are 50 or 52 ohms, and 75 ohms, although other impedances are available for specific applications. The 50 / 52 ohm cables are widely used for industrial and commercial two-way radio frequency applications (including radio, and telecommunications), although 75 ohms is commonly used for broadcast television and radio.

Coax cable is often used to carry data/signals from an antenna to a receiver—from a satellite dish to a satellite receiver, from a television antenna to a television receiver, from a radio mast to a radio receiver, etc. In many cases, the same single coax cable carries power in the opposite direction, to the antenna, to power the low-noise amplifier. In some cases a single coax cable carries (unidirectional) power and bidirectional data/signals, as in DiSEqC.

Types[edit]

Hard line[edit]

1 ⁵⁄₈ in (41 mm) flexible line

1-5/8" Heliax coaxial cable

Hard line is used in broadcasting as well as many other forms of radio communication. It is a coaxial cable constructed using round copper, silver or gold tubing or a combination of such metals as a shield. Some lower-quality hard line may use aluminum shielding, aluminum however is easily oxidized and unlike silver oxide, aluminum oxide drastically loses effective conductivity. Therefore, all connections must be air and water tight. The center conductor may consist of solid copper, or copper-plated aluminum. Since skin effect is an issue with RF, copper plating provides sufficient surface for an effective conductor. Most varieties of hardline used for external chassis or when exposed to the elements have a PVC jacket; however, some internal applications may omit the insulation jacket. Hard line can be very thick, typically at least a half inch or 13 mm and up to several times that, and has low loss even at high power. These large-scale hard lines are almost always used in the connection between a transmitter on the ground and the antenna or aerial on a tower. Hard line may also be known by trademarked names such as Heliax (CommScope),^[44] or Cablewave (RFS/Cablewave).^[45] Larger varieties of hardline may have a center conductor that is constructed from either rigid or corrugated copper tubing. The dielectric in hard line may consist of polyethylene foam, air, or a pressurized gas such as nitrogen or desiccated air (dried air). In gas-charged lines, hard plastics such as nylon are used as spacers to separate the inner and outer conductors. The addition of these gases into the dielectric space reduces moisture contamination, provides a stable dielectric constant, and provides a reduced risk of internal arcing. Gas-filled hardlines are usually used on high-power RF transmitters such as television or radio broadcasting, military transmitters, and high-power amateur radio applications but may also be used on some critical lower-power applications such as those in the microwave bands. However, in the microwave region, waveguide is more often used than hard line for transmitter-to-antenna, or antenna-to-receiver applications. The various shields used in hardline also differ; some forms use rigid tubing, or pipe, while others may use a corrugated tubing, which makes bending easier, as well as reduces kinking when the cable is bent to conform. Smaller varieties of hard line may be used internally in some high-frequency applications, in particular in equipment within the microwave range, to reduce interference between stages of the device.

Radiating[edit]

Radiating or leaky cable is another form of coaxial cable which is constructed in a similar fashion to hard line, however it is constructed with tuned slots cut into the shield. These slots are tuned to the specific RF wavelength of operation or tuned to a specific radio frequency band. This type of cable is to provide a tuned bi-directional "desired" leakage effect between transmitter and receiver. It is often used in elevator shafts, US Navy Ships, underground transportation tunnels and in other areas where an antenna is not feasible. One example of this type of cable is Radiax (CommScope).^[46]

RG-6[edit]

RG-6 is available in four different types designed for various applications. In addition, the core may be copper clad steel (CCS) or bare solid copper (BC). "Plain" or "house" RG-6 is designed for indoor or external house wiring. "Flooded" cable is infused with waterblocking gel for use in underground conduit or direct burial. "Messenger" may contain some waterproofing but is distinguished by the addition of a steel messenger wire along its length to carry the tension involved in an aerial drop from a utility pole. "Plenum" cabling is expensive and comes with a special Teflon-based outer jacket designed for use in ventilation ducts to meet fire codes. It was developed since the plastics used as the outer jacket and inner insulation in many "Plain" or "house" cabling gives off poison gas when burned.

Triaxial cable[edit]

Triaxial cable or triax is coaxial cable with a third layer of shielding, insulation and sheathing. The outer shield, which is earthed (grounded), protects the inner shield from electromagnetic interference from outside sources.

Twin-axial cable[edit]

Twin-axial cable or twinax is a balanced, twisted pair within a cylindrical shield. It allows a nearly perfect differential signal which is both shielded and balanced to pass through. Multi-conductor coaxial cable is also sometimes used.

Semi-rigid[edit]

Semi-Rigid coax assembly

Semi-Rigid coax installed in an Agilent N9344C 20GHz spectrum analyser

Semi-rigid cable is a coaxial form using a solid copper outer sheath. This type of coax offers superior screening compared to cables with a braided outer conductor, especially at higher frequencies. The major disadvantage is that the cable, as its name implies, is not very flexible, and is not intended to be flexed after initial forming. (See "hard line")

Conformable cable is a flexible reformable alternative to semi-rigid coaxial cable used where flexibility is required. Conformable cable can be stripped and formed by hand without the need for specialized tools, similar to standard coaxial cable.

Rigid line[edit]

Rigid line is a coaxial line formed by two copper tubes maintained concentric every other meter using PTFE-supports. Rigid lines cannot be bent, so they often need elbows. Interconnection with rigid line is done with an inner bullet/inner support and a flange or connection kit. Typically, rigid lines are connected using standardised EIA RF Connectors whose bullet and flange sizes match the standard line diameters. For each outer diameter, either 75 or 50 ohm inner tubes can be obtained. Rigid line is commonly used indoors for interconnection between high power transmitters and other RF-components, but more rugged rigid line with weatherproof flanges is used outdoors on antenna masts, etc. In the interests of saving weight and costs, on masts and similar structures the outer line is often aluminium, and special care must be taken to prevent corrosion. With a flange connector, it is also possible to go from rigid line to hard line. Many broadcasting antennas and antenna splitters use the flanged rigid line interface even when connecting to flexible coaxial cables and hard line. Rigid line is produced in a number of different sizes:

Cables used in the UK[edit]

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At the start of analogue satellite TV broadcasts in the UK by BskyB, a 75 ohm cable referred to as RG6 was used. This cable had a 1 mm copper core, air-spaced polyethylene dielectric and copper braid on an aluminium foil shield. When installed outdoors without protection, the cable was affected by UV radiation, which cracked the PVC outer sheath and allowed moisture ingress. The combination of copper, aluminium, moisture and air caused rapid corrosion, sometimes resulting in a 'snake swallowed an egg' appearance. Consequently, despite the higher cost, the RG6 cable was dropped in favour of CT100 when BSKYB launched its digital broadcasts.

From around 1999 to 2005 (when CT100 manufacturer Raydex went out of business), CT100 remained the 75 ohm cable of choice for satellite TV and especially BskyB. It had an air-spaced polyethylene dielectric, a 1 mm solid copper core and copper braid on copper foil shield. CT63 was a thinner cable in 'shotgun' style, meaning that it was two cables moulded together and was used mainly by BskyB for the twin connection required by the Sky+ satellite TV receiver, which incorporated a hard drive recording system and a second, independent tuner.

In 2005, these cables were replaced by WF100 and WF65, respectively, manufactured by Webro and having a similar construction but a foam dielectric that provided the same electrical performance as air-spaced but was more robust and less likely to be crushed.

At the same time, with the price of copper steadily rising, the original RG6 was dropped in favour of a construction that used a copper-clad steel core and aluminium braid on aluminium foil. Its lower price made it attractive to aerial installers looking for a replacement for the so-called low-loss cable traditionally used for UK terrestrial aerial installations. This cable had been manufactured with a decreasing number of strands of braid, as the price of copper increased, such that the shielding performance of cheaper brands had fallen to as low as 40 percent. With the advent of digital terrestrial transmissions in the UK, this low-loss cable was no longer suitable.

The new RG6 still performed well at high frequencies because of the skin effect in the copper cladding. However, the aluminium shield had a high DC resistance and the steel core an even higher one. The result is that this type of cable could not reliably be used in satellite TV installations, where it was required to carry a significant amount of current, because the voltage drop affected the operation of the low noise block downconverter (LNB) on the dish.

A problem with all the aforementioned cables, when passing current, is that electrolytic corrosion can occur in the connections unless moisture and air are excluded. Consequently, various solutions to exclude moisture have been proposed. The first was to seal the connection by wrapping it with self-amalgamating rubberised tape, which bonds to itself when activated by stretching. The second proposal, by the American Channel Master company (now owned by Andrews corp.) at least as early as 1999, was to apply silicone greaseto the wires making connection. The third proposal was to fit a self-sealing plug to the cable. All of these methods are reasonably successful if implemented correctly.

Interference and troubleshooting[edit]

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Coaxial cable insulation may degrade, requiring replacement of the cable, especially if it has been exposed to the elements on a continuous basis. The shield is normally grounded, and if even a single thread of the braid or filament of foil touches the center conductor, the signal will be shorted causing significant or total signal loss. This most often occurs at improperly installed end connectors and splices. Also, the connector or splice must be properly attached to the shield, as this provides the path to ground for the interfering signal.

Despite being shielded, interference can occur on coaxial cable lines. Susceptibility to interference has little relationship to broad cable type designations (e.g. RG-59, RG-6) but is strongly related to the composition and configuration of the cable's shielding. For cable television, with frequencies extending well into the UHF range, a foil shield is normally provided, and will provide total coverage as well as high effectiveness against high-frequency interference. Foil shielding is ordinarily accompanied by a tinned copper or aluminum braid shield, with anywhere from 60 to 95% coverage. The braid is important to shield effectiveness because (1) it is more effective than foil at preventing low-frequency interference, (2) it provides higher conductivity to ground than foil, and (3) it makes attaching a connector easier and more reliable. "Quad-shield" cable, using two low-coverage aluminum braid shields and two layers of foil, is often used in situations involving troublesome interference, but is less effective than a single layer of foil and single high-coverage copper braid shield such as is found on broadcast-quality precision video cable.

In the United States and some other countries, cable television distribution systems use extensive networks of outdoor coaxial cable, often with in-line distribution amplifiers. Leakage of signals into and out of cable TV systems can cause interference to cable subscribers and to over-the-air radio services using the same frequencies as those of the cable system.

History[edit]

Early coaxial antenna feedline of 50 kW radio station WNBC, New York, in 1930s

AT&T coaxial cable trunkline installed between East Coast and Midwest in 1948. Each of the 8 coaxial subcables could carry 480 telephone calls or one television channel.

• 1880 — Coaxial cable patented in England by Oliver Heaviside, patent no. 1,407.^[47]

• 1884 — Siemens & Halske patent coaxial cable in Germany (Patent No. 28,978, 27 March 1884).^[48]

• 1894 — Nikola Tesla (U.S. Patent 514,167)

• 1929 — First modern coaxial cable patented by Lloyd Espenschied and Herman Affel of AT&T's Bell Telephone Laboratories.^[49]

• 1936 — First closed circuit transmission of TV pictures on coaxial cable, from the 1936 Summer Olympics in Berlin to Leipzig.^[50]

• 1936 — World's first underwater coaxial cable installed between Apollo Bay, near Melbourne, Australia, and Stanley, Tasmania. The 300 km (190 mi) cable can carry one 8.5-kHz broadcast channel and seven telephone channels.^[51]

• 1936 — AT&T installs experimental coaxial telephone and television cable between New York and Philadelphia, with automatic booster stations every ten miles (16 km). Completed in December, it can transmit 240 telephone calls simultaneously.^[52][53]

• 1936 — Coaxial cable laid by the General Post Office (now BT) between London and Birmingham, providing 40 telephone channels.^[54][55]

• 1941 — First commercial use in USA by AT&T, between Minneapolis, Minnesota and Stevens Point, Wisconsin. L1 system with capacity of one TV channel or 480 telephone circuits.

• 1949 — On January 11, eight stations on the US East Coast and seven Midwestern stations are linked via a long-distance coaxial cable.^[56]

• 1956 — First transatlantic coaxial cable laid, TAT-1.^[57][58]

• 1962 — 960 km (600 mi) Sydney–Melbourne co-axial cable commissioned, carrying 3 x 1,260 simultaneous telephone connections, and-or simultaneous inter-city television transmission.^[59][60]