Coaxial Cable

Coaxial cable structure

Coaxial cable is an electrical cable with a defined geometry for carrying high-frequency signals. It uses concentric conductors that share one axis, which helps control the electromagnetic field, attenuation, and susceptibility to external interference. Usable frequency band and attenuation depend on the cable construction and its specified operating limits. Nominal impedance alone does not specify bandwidth.

Main components

• Inner Conductor (Core): Central wire, typically solid copper or copper-clad steel, which carries the high-frequency signal.
• Insulator (Dielectric):Layer of insulating material surrounding the core, electrically separating it from the shield. The dielectric properties (e.g., polyethylene, Teflon) set the cable's electrical parameters.
• Outer conductor (shield): Metallic layer, often in the form of a braid of thin copper wires or aluminum foil, surrounding the dielectric. It serves as the second conductor of the circuit and protects the core from external Electromagnetic Interference (EMI).
• Protective Jacket: The outermost layer, typically made of PVC, providing mechanical protection and resistance to environmental conditions.

How a coaxial cable carries a TEM wave

The coaxial structure confines most of the electromagnetic energy between the inner and outer conductors. In its intended operating range, the signal propagates mainly as Transverse Electromagnetic Wave (TEM).

For a TEM wave in coaxial cable:

• Lines of Electric Field $(E)$ radiate from the inner conductor to the outer shield.
• Lines of Magnetic Field $(H)$ form concentric circles around the inner conductor.
• Both fields are perpendicular to each other and to the signal propagation direction along the cable axis $(z)$.

Field confinement contributes to shielding and reduces leakage of signal energy outside the cable. The actual performance also depends on the shield construction, connectors, and termination.

Primary Electrical Parameters (RLCG)

For a homogeneous coaxial line, the behavior of the path is described by four distributed primary parameters, given per unit length (e.g., per meter or kilometer).

• Resistance $(R)$: Represents ohmic losses in the inner and outer conductors. Increases with frequency due to skin effect.
• Inductance $(L)$: Results from magnetic field energy stored around and within the conductors. Consists of frequency-dependent internal part and geometry-dependent dominant external part.
• Capacitance $(C)$: Results from electric field energy stored in the dielectric between conductors. Is determined by cable geometry (diameter ratio) and dielectric permittivity ($\epsilon_r$). Formula: $C = \frac{2 \pi \epsilon_0 \epsilon_r}{\ln(\frac{D}{d})}$
• Conductance $(G)$: Represents energy losses in the dielectric insulator due to leakage current. Increases with frequency and is proportional to the dielectric loss tangent of the dielectric.

Secondary Wave Parameters

Although the RLCG parameters fully describe the line, in practice it's more convenient to work with secondary (wave) parameters that directly describe how the signal propagates.

Characteristic Impedance $Z_c$

Characteristic impedance is the impedance that the transmission line presents to a propagating wave. Matching the source, line, connectors, and load reduces reflections; maximum power transfer also depends on the source and load conditions.

For a homogeneous coaxial cable with a dielectric of relative permittivity $\epsilon_r$, the lossless approximation is $Z_0 \approx \frac{60}{\sqrt{\epsilon_r}} \ln\left(\frac{D}{d}\right)$, where $D$ is the inner diameter of the outer conductor and $d$ is the diameter of the inner conductor.

Standard impedances for coaxial cables are 50 Ω (used in RF test equipment and many radio systems) and 75 Ω (used in video and television systems). In idealized air-dielectric designs, the theoretical trade-off is near 77 Ω for minimum attenuation and near 30 Ω for maximum power handling. Practical cables use standardized values together with their specified dielectric and geometry.

Propagation Constant $\gamma$

This complex number describes how the amplitude and phase of a signal change during propagation along the line. Formula: $\gamma = \sqrt{(R + j\omega L)(G + j\omega C)}$. It consists of two parts:

• Attenuation Constant $\alpha$: Real part of $\gamma$, measured in nepers/m or dB/m. Describes exponential decay of signal amplitude with distance.
• Phase Constant $\beta$: Imaginary part of $\gamma$, measured in radians/m. Describes the rate of phase change of the signal with distance. It is related to the wavelength in the cable: $\beta = \frac{2\pi}{\lambda_{\text{cable}}}$.

Shielding Effectiveness

Coaxial cable shielding is described with several electrical measures:

• Transfer impedance $Z_t$: Measure of how current on the inner side of the shield couples to the outer side and induces a voltage there. It is measured in $\Omega/\text{m}$; a lower value indicates better shielding.
• Shielding effectiveness (SE): Measured in decibels (dB), it is the ratio of incident external field intensity to the field intensity that reaches the inner conductor through the shield. A higher value in dB indicates better shielding.

  Formula: $SE_{\text{[dB]}} = 20 \cdot \log_{10} \left( \frac{E_{\text{incident}}}{E_{\text{internal}}} \right)$

Popular Applications

Coaxial cables are used in a wide range of applications, including:

• Cable television distribution (CATV)
• Satellite television installations (connecting dish to receiver)
• Antenna feed lines (e.g., in amateur radio, cellular base stations)
• Legacy computer networks (e.g., 10Base-2 "Thinnet" Ethernet)
• High-frequency test and measurement equipment
• Video connections (e.g., composite, SDI)