Physical parameters

In the following section, these symbols are used:

• Length of the cable, ${\displaystyle \ \ell ~.}$
• Outside diameter of inner conductor, ${\displaystyle \ d~.}$
• Inside diameter of the shield, ${\displaystyle \ D~.}$
• Dielectric constant of the insulator, ${\displaystyle \ \epsilon ~.}$ The dielectric constant is often quoted as the relative dielectric constant ${\displaystyle \ \epsilon _{\mathsf {r}}\ }$ referred to the dielectric constant of free space ${\displaystyle \ \epsilon _{\mathsf {o}}\$ :} ${\displaystyle \ \epsilon =\epsilon _{\mathsf {r}}\ \epsilon _{\mathsf {o}}~.}$ 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 ${\displaystyle \ \epsilon _{\mathsf {eff}}\ }$ is often used.
• Magnetic permeability of the insulator, ${\displaystyle \ \mu ~.}$ Permeability is often quoted as the relative permeability ${\displaystyle \ \mu _{\mathsf {r}}\ }$ referred to the permeability of free space ${\displaystyle \ \mu _{\mathsf {o}}\$ :} ${\displaystyle \ \mu =\mu _{\mathsf {r}}\ \mu _{\mathsf {o}}~.}$ The relative permeability will almost always be 1.

Fundamental electrical parameters

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

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

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

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

• 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.

Derived electrical parameters

• Characteristic impedance in ohms (Ω). The complex impedance Z_o of an infinite length of transmission line is:

${\displaystyle Z_{\mathsf {o}}={\sqrt {{\frac {R+sL\ }{G+sC\ }}\ }}}$

Where R is the resistance per unit length, L is the inductance per unit length, G is the conductance per unit length of the dielectric, C is the capacitance per unit length, and s = jω = j2πf is the frequency. The "per unit length" dimensions cancel out in the impedance formula.

At DC the two reactive terms are zero, so the impedance is real-valued, and is extremely high. It looks like

${\displaystyle Z_{\mathsf {DC}}={\sqrt {{\frac {\ R\ }{G}}\ }}~.}$

With increasing frequency, the reactive components take effect and the impedance of the line is complex-valued. At very low frequencies (audio range, of interest to telephone systems) G is typically much smaller than sC, so the impedance at low frequencies is

${\displaystyle Z_{\mathsf {LowFreq}}\approx {\sqrt {{\frac {R}{\ sC\ }}\ }}\ ,}$

which has a phase value of -45 degrees.

At higher frequencies, the reactive terms usually dominate R and G, and the cable impedance again becomes real-valued. That value is Z_o, the characteristic impedance of the cable:

${\displaystyle Z_{\mathsf {o}}={\sqrt {{\frac {sL}{\ sC\ }}\ }}={\sqrt {{\frac {L}{\ C\ }}\ }}~.}$

Assuming the dielectric properties of the material inside the cable do not vary appreciably over the operating range of the cable, the characteristic impedance is frequency independent above about five times the shield cutoff frequency. For typical coaxial cables, the shield cutoff frequency is 600 Hz (for RG-6A) to 2,000 Hz (for RG-58C).^[10]

The parameters L and C are determined from the ratio of the inner (d) and outer (D) diameters and the dielectric constant (ε). The characteristic impedance is given by^[11]

${\displaystyle Z_{\mathsf {o}}={\frac {1}{\ 2\pi \ }}{\sqrt {{\frac {\mu }{\ \epsilon \ }}\ }}\ \ln \left({\frac {D}{\ d\ }}\right)\approx {\frac {\ 59.96\ {\mathsf {\Omega }}\ }{\sqrt {\epsilon _{\mathsf {r}}\ }}}\ln \left({\frac {D}{\ d\ }}\right)\approx {\frac {\ 138\ {\mathsf {\Omega }}\ }{\sqrt {\epsilon _{\mathsf {r}}\ }}}\log _{10}\left({\frac {D}{\ d\ }}\right)~.}$

• Attenuation (loss) per unit length, in decibels per meter. This is dependent on the loss in the dielectric material filling the cable, and resistive losses in the center conductor and outer shield. These losses are frequency dependent, the losses becoming higher as the frequency increases. Skin effect losses in the conductors can be reduced by increasing the diameter of the cable. A cable with twice the diameter will have half the skin effect resistance. Ignoring dielectric and other losses, the larger cable would halve the dB/meter loss. In designing a system, engineers consider not only the loss in the cable but also the loss in the connectors.
• Velocity of propagation, in meters per second. The velocity of propagation depends on the dielectric constant and permeability (which is usually 1).

${\displaystyle v={\frac {1}{\ {\sqrt {\epsilon \mu \ }}\ }}={\frac {c}{\ {\sqrt {\epsilon _{\mathsf {r}}\mu _{\mathsf {r}}\ }}\ }}}$

• Single-mode band. In coaxial cable, the dominant mode (the mode with the lowest cutoff frequency) is the TEM mode,^[7] which has a cutoff frequency of zero; it propagates all the way down to DC. The mode with the next lowest cutoff is the TE₁₁ mode. This mode has one 'wave' (two reversals of polarity) in going around the circumference of the cable. To a good approximation, the condition for the TE₁₁ mode to propagate is that the wavelength in the dielectric is no longer than the average circumference of the insulator; that is that the frequency is at least

${\displaystyle f_{\mathsf {c}}\approx {\frac {1}{\ \pi \left({\frac {D+d}{2}}\right){\sqrt {\mu \epsilon \ }}}}={\frac {c}{\ \pi \left({\frac {D+d}{2}}\right){\sqrt {\mu _{\mathsf {r}}\epsilon _{\mathsf {r}}\ }}}}~.}$

Hence, the cable is single-mode from DC up to this frequency, and might in practice be used up to 90%^[12] of this frequency.

• Peak Voltage. The peak voltage is set by the breakdown voltage of the insulator.:^[13]

${\displaystyle V_{\mathsf {p}}=\ E_{\mathsf {d}}\ {\frac {d}{2}}\ \ln \left({\frac {\ D\ }{d}}\right)}$

where

V_p is the peak voltage

E_d is the insulator's breakdown voltage in volts per meter

d is the inner diameter in meters

D is the outer diameter in meters

The calculated peak voltage is often reduced by a safety factor.

Choice of impedance

The best coaxial cable impedances were experimentally determined at Bell Laboratories in 1929 to be 77 Ω for low-attenuation, 60 Ω for high-voltage, and 30 Ω for high-power. For a coaxial cable with air dielectric and a shield of a given inner diameter, the attenuation is minimized by choosing the diameter of the inner conductor to give a characteristic impedance of 76.7 Ω.^[14] When more common dielectrics are considered, the lowest insertion loss impedance drops down to a value between 52 and 64 Ω. Maximum power handling is achieved at 30 Ω.^[15]

The approximate impedance required to match a centre-fed dipole antenna in free space (i.e., a dipole without ground reflections) is 73 Ω, so 75 Ω coax was commonly used for connecting shortwave antennas to receivers. These typically involve such low levels of RF power that power-handling and high-voltage breakdown characteristics are unimportant when compared to attenuation. Likewise with CATV, although many broadcast TV installations and CATV headends use 300 Ω folded dipole antennas to receive off-the-air signals, 75 Ω coax makes a convenient 4:1 balun transformer for these as well as possessing low attenuation.

The arithmetic mean between 30 Ω and 77 Ω is 53.5 Ω; the geometric mean is 48 Ω. The selection of 50 Ω as a compromise between power-handling capability and attenuation is in general cited as the reason for the number.^[14] 50 Ω also works out tolerably well because it corresponds approximately to the feedpoint impedance of a half-wave dipole, mounted approximately a half-wave above "normal" ground (ideally 73 Ω, but reduced for low-hanging horizontal wires).

RG-62 is a 93 Ω coaxial cable originally used in mainframe computer networks in the 1970s and early 1980s (it was the cable used to connect IBM 3270 terminals to IBM 3274/3174 terminal cluster controllers). Later, some manufacturers of LAN equipment, such as Datapoint for ARCNET, adopted RG-62 as their coaxial cable standard. The cable has the lowest capacitance per unit-length when compared to other coaxial cables of similar size.

All of the components of a coaxial system should have the same impedance to avoid internal reflections at connections between components (see Impedance matching). Such reflections may cause signal attenuation. They introduce standing waves, which increase losses and can even result in cable dielectric breakdown with high-power transmission. In analog video or TV systems, reflections cause ghosting in the image; multiple reflections may cause the original signal to be followed by more than one echo. If a coaxial cable is open (not connected at the end), the termination has nearly infinite resistance, which causes reflections. If the coaxial cable is short-circuited, the termination resistance is nearly zero, which causes reflections with the opposite polarity. Reflections will be nearly eliminated if the coaxial cable is terminated in a pure resistance equal to its impedance.

Signal leakage

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. In-channel ingress can be digitally removed by ingress cancellation.

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^[17] which is referenced in IEC 61917.^[18]

Ground loops

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

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.

Common mode current and radiation

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. They are the opposite of the desired "push-pull" differential signalling currents, where the signal currents on the inner and outer conductor are equal and opposite.

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.

Higher impedance at audio frequencies

The characteristic impedance formula above is a good approximation at radio frequencies however for frequencies below 100 kHz (such as audio) it becomes important to use the complete telegrapher's equation:

${\displaystyle Z_{\text{o}}={\sqrt {{\frac {R+j\omega L}{G+j\omega C}}\ }}}$

Applying this formula to typical 75 ohm coax we find the measured impedance across the audio spectrum will range from ~150 ohms to ~5K ohms, much higher than nominal. The velocity of propagation also slows considerably. Thus we can expect coax cable impedances to be consistent at RF frequencies but variable across audio frequencies. This effect was manifested when trying to send a plain voice signal across the transatlantic telegraph cable, with poor results.^[19][20]

Hard line

1+5⁄8 in (41 mm) flexible line with (mostly) air dielectric

1+5⁄8 in (41 mm) Heliax coaxial cable with FPE foamed polyethylene dielectric

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 hard line 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

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).^[44]

RG-6

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 water-blocking 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 poisonous gas when burned.

Triaxial cable

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.

Semi-rigid

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

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: