Co-axial cable

Coaxial cable, or coax (pronounced /ˈkoʊ.æks/), is a type of electrical cable consisting of an inner conductor surrounded by a concentric conducting shield, with the two separated by a dielectric (insulating material); many coaxial cables also have a protective outer sheath or jacket. The term coaxial refers to the inner conductor and the outer shield sharing a geometric axis.

Coaxial cable is a type of transmission line, used to carry high-frequency electrical signals with low losses. It is used in such applications as telephone trunk lines, broadband internet networking cables, high-speed computer data busses, cable television signals, and connecting radio transmitters and receivers to their antennas. It differs from other shielded cables because the dimensions of the cable and connectors are controlled to give a precise, constant conductor spacing, which is needed for it to function efficiently as a transmission line.

In his 1880 British patent, Oliver Heaviside showed how coaxial cable could eliminate signal interference between parallel cables.

Coaxial cable was used in the first (1858) and following transatlantic cable installations, but its theory was not described until 1880 by English physicist, engineer, and mathematician Oliver Heaviside, who patented the design in that year (British patent No. 1,407).^[1]

Applications

Coaxial cable is used as a transmission line for radio frequency signals. Its applications include feedlines connecting radio transmitters and receivers to their antennas, computer network (e.g., Ethernet) connections, digital audio (S/PDIF), and distribution of cable television signals. One advantage of coaxial over other types of radio transmission line is that in an ideal coaxial cable the electromagnetic field carrying the signal exists only in the space between the inner and outer conductors. This allows coaxial cable runs to be installed next to metal objects such as gutters without the power losses that occur in other types of transmission lines. Coaxial cable also provides protection of the signal from external electromagnetic interference.

Description

Coaxial cable conducts electrical signals using an inner conductor (usually a solid copper, stranded copper or copper-plated steel wire) surrounded by an insulating layer and all enclosed by a shield, typically one to four layers of woven metallic braid and metallic tape.^[2] The cable is protected by an outer insulating jacket. Normally, the outside of the shield is kept at ground potential and a signal carrying voltage is applied to the center conductor. When using differential signaling, coaxial cable provides an advantage of equal push-pull currents on the inner conductor and inside of the outer conductor that restrict the signal's electric and magnetic fields to the dielectric, with little leakage outside the shield.^{[citation needed]} Further, electric and magnetic fields outside the cable are largely kept from interfering with signals inside the cable, if unequal currents are filtered out at the receiving end of the line. This property makes coaxial cable a good choice both for carrying weak signals that cannot tolerate interference from the environment, and for stronger electrical signals that must not be allowed to radiate or couple into adjacent structures or circuits.^[3] Larger diameter cables and cables with multiple shields have less leakage.

Common applications of coaxial cable include video and CATV distribution, RF and microwave transmission, and computer and instrumentation data connections.^[4]

The characteristic impedance of the cable ( $Z 0$ ) is determined by the dielectric constant of the inner insulator and the radii of the inner and outer conductors. In radio frequency systems, where the cable length is comparable to the wavelength of the signals transmitted, a uniform cable characteristic impedance is important to minimize loss. The source and load impedances are chosen to match the impedance of the cable to ensure maximum power transfer and minimum standing wave ratio. Other important properties of coaxial cable include attenuation as a function of frequency, voltage handling capability, and shield quality.^[3]

Construction

Coaxial cable design choices affect physical size, frequency performance, attenuation, power handling capabilities, flexibility, strength, and cost. The inner conductor might be solid or stranded; stranded is more flexible. To get better high-frequency performance, the inner conductor may be silver-plated. Copper-plated steel wire is often used as an inner conductor for cable used in the cable TV industry.^[5]

The insulator surrounding the inner conductor may be solid plastic, a foam plastic, or air with spacers supporting the inner wire. The properties of the dielectric insulator determine some of the electrical properties of the cable. A common choice is a solid polyethylene (PE) insulator, used in lower-loss cables. Solid Teflon (PTFE) is also used as an insulator, and exclusively in plenum-rated cables.^{[citation needed]} Some coaxial lines use air (or some other gas) and have spacers to keep the inner conductor from touching the shield.

Many conventional coaxial cables use braided copper wire forming the shield. This allows the cable to be flexible, but it also means there are gaps in the shield layer, and the inner dimension of the shield varies slightly because the braid cannot be flat. Sometimes the braid is silver-plated. For better shield performance, some cables have a double-layer shield.^[5] The shield might be just two braids, but it is more common now to have a thin foil shield covered by a wire braid. Some cables may invest in more than two shield layers, such as "quad-shield", which uses four alternating layers of foil and braid. Other shield designs sacrifice flexibility for better performance; some shields are a solid metal tube. Those cables cannot be bent sharply, as the shield will kink, causing losses in the cable. When a foil shield is used a small wire conductor incorporated into the foil makes soldering the shield termination easier.^{[examples needed]}

For high-power radio-frequency transmission up to about 1 GHz, coaxial cable with a solid copper outer conductor is available in sizes of 0.25 inch upward. The outer conductor is corrugated like a bellows to permit flexibility and the inner conductor is held in position by a plastic spiral to approximate an air dielectric.^[5] One brand name for such cable is Heliax.^[6]

Coaxial cables require an internal structure of an insulating (dielectric) material to maintain the spacing between the center conductor and shield. The dielectric losses increase in this order: Ideal dielectric (no loss), vacuum, air, polytetrafluoroethylene (PTFE), polyethylene foam, and solid polyethylene. An inhomogeneous dielectric needs to be compensated by a non-circular conductor to avoid current hot-spots.

While many cables have a solid dielectric, many others have a foam dielectric that contains as much air or other gas as possible to reduce the losses by allowing the use of a larger diameter center conductor. Foam coax will have about 15% less attenuation but some types of foam dielectric can absorb moisture—especially at its many surfaces—in humid environments, significantly increasing the loss. Supports shaped like stars or spokes are even better but more expensive and very susceptible to moisture infiltration. Still more expensive were the air-spaced coaxials used for some inter-city communications in the mid-20th century. The center conductor was suspended by polyethylene discs every few centimeters. In some low-loss coaxial cables such as the RG-62 type, the inner conductor is supported by a spiral strand of polyethylene, so that an air space exists between most of the conductor and the inside of the jacket. The lower dielectric constant of air allows for a greater inner diameter at the same impedance and a greater outer diameter at the same cutoff frequency, lowering ohmic losses. Inner conductors are sometimes silver-plated to smooth the surface and reduce losses due to skin effect.^[5] A rough surface extends the current path and concentrates the current at peaks, thus increasing ohmic loss.

The insulating jacket can be made from many materials. A common choice is PVC, but some applications may require fire-resistant materials. Outdoor applications may require the jacket to resist ultraviolet light, oxidation, rodent damage, or direct burial. Flooded coaxial cables use a water-blocking gel to protect the cable from water infiltration through minor cuts in the jacket. For internal chassis connections the insulating jacket may be omitted.^{[examples needed]}

Signal propagation

Twin-lead transmission lines have the property that the electromagnetic wave propagating down the line extends into the space surrounding the parallel wires. These lines have low loss, but also have undesirable characteristics. They cannot be bent, tightly twisted, or otherwise shaped without changing their characteristic impedance, causing reflection of the signal back toward the source. They also cannot be buried or run along or attached to anything conductive, as the extended fields will induce currents in the nearby conductors causing unwanted radiation and detuning of the line. Standoff insulators are used to keep them away from parallel metal surfaces. Coaxial lines largely solve this problem by confining virtually all of the electromagnetic wave to the area inside the cable. Coaxial lines can therefore be bent and moderately twisted without negative effects, and they can be strapped to conductive supports without inducing unwanted currents in them, so long as provisions are made to ensure differential signalling push-pull currents in the cable.

In radio-frequency applications up to a few gigahertz, the wave propagates primarily in the transverse electric magnetic (TEM) mode, which means that the electric and magnetic fields are both perpendicular to the direction of propagation. However, above a certain cutoff frequency, transverse electric (TE) or transverse magnetic (TM) modes can also propagate, as they do in a hollow waveguide. It is usually undesirable to transmit signals above the cutoff frequency, since it may cause multiple modes with different phase velocities to propagate, interfering with each other. The outer diameter is roughly inversely proportional to the cutoff frequency. A propagating surface-wave mode that only involves the central conductor also exists, but is effectively suppressed in coaxial cable of conventional geometry and common impedance. Electric field lines for this TM mode have a longitudinal component and require line lengths of a half-wavelength or longer.

Coaxial cable may be viewed as a type of waveguide. Power is transmitted through the radial electric field and the circumferential magnetic field in the TEM mode. This is the dominant mode from zero frequency (DC) to an upper limit determined by the electrical dimensions of the cable.^[7]

Connectors

A male F-type connector used with common RG-6 cable

A male N-type connector

Coaxial connectors are designed to maintain a coaxial form across the connection and have the same impedance as the attached cable.^[5] Connectors are usually plated with high-conductivity metals such as silver or tarnish-resistant gold. Due to the skin effect, the RF signal is only carried by the plating at higher frequencies and does not penetrate to the connector body. Silver however tarnishes quickly and the silver sulfide that is produced is poorly conductive, degrading connector performance, making silver a poor choice for this application.^[8]

Important parameters

Coaxial cable is a particular kind of transmission line, so the circuit models developed for general transmission lines are appropriate. See Telegrapher's equation.

Physical parameters

In the following section, these symbols are used:

Length of the cable, $\ \ell ~.$
Outside diameter of inner conductor, $\ d~.$
Inside diameter of the shield, $\ D~.$
Dielectric constant of the insulator, $\ \epsilon ~.$ The dielectric constant is often quoted as the relative dielectric constant $\ \epsilon _{\mathsf {r}}\$ referred to the dielectric constant of free space $\ \epsilon _{\mathsf {o}}\ :$ $\ \epsilon =\epsilon _{\mathsf {r}}\ \epsilon _{\mathsf {o}}~.$ When the insulator is a mixture of different dielectric materials (e.g., polyethylene foam is a mixture of polyethylene and air), then the term effective dielectric constant $\ \epsilon _{\mathsf {eff}}\$ is often used.
Magnetic permeability of the insulator, $\ \mu ~.$ Permeability is often quoted as the relative permeability $\ \mu _{\mathsf {r}}\$ referred to the permeability of free space $\ \mu _{\mathsf {o}}\ :$ $\ \mu =\mu _{\mathsf {r}}\ \mu _{\mathsf {o}}~.$ The relative permeability will almost always be $1$ .

Fundamental electrical parameters

Shunt capacitance per unit length, in farads per metre.^[9]

C={\frac {2\pi \epsilon }{\ \ln \left({\frac {\ D\ }{d}}\right)\ }}={\frac {2\pi \epsilon _{\mathsf {o}}\epsilon _{\mathsf {r}}}{\ \ln \left({\frac {\ D\ }{d}}\right)\ }}

Series inductance per unit length, in henries per metre, considering the central conductor to be a thin hollow cylinder (due to skin effect).

L={\frac {\mu }{\ 2\pi \ }}\ \ln \left({\frac {\ D\ }{d}}\right)={\frac {\ \mu _{\mathsf {o}}\mu _{\mathsf {r}}\ }{2\pi }}\ \ln \left({\frac {\ D\ }{d}}\right)

Series resistance per unit length, in ohms per metre. The resistance per unit length is just the resistance of inner conductor and the shield at low frequencies. At higher frequencies, skin effect increases the effective resistance by confining the conduction to a thin layer of each conductor.
Shunt conductance per unit length, in siemens per metre. The shunt conductance is usually very small because insulators with good dielectric properties are used (a very low loss tangent). At high frequencies, a dielectric can have a significant resistive loss.