Signal Propogation in Coaxial Cable

Open wire 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, twisted or otherwise shaped without changing their characteristic impedance. They also cannot be 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. Coaxial lines solve this problem by confining the electromagnetic wave to the area inside the cable, between the center conductor and the shield. The transmission of energy in the line occurs totally through the dielectric inside the cable between the conductors. 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. In radio-frequency applications up to a few gigahertz, the wave propagates only 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) and/or transverse magnetic (TM) modes can also propagate, as they do in a 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.

The outer conductor can also be made of (in order of decreasing leakage and in this case degree of balance): double shield, wound foil, woven tape, braid. The ohmic losses in the conductor increase in this order: Ideal conductor (no loss), superconductor, silver, copper. It is further increased by rough surface (in the order of the skin depth, lateral: current hot spots, longitudinal: long current path) for example due to woven braid, multistranded conductors or a corrugated tube as a conductor) and impurities especially oxygen in the metal (due to a lack of a protective coating). Litz wire is used between 1 kHz and 1 MHz to reduce ohmic losses. 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. It is further increased by impurities like water. In typical applications the loss in polyethylene is comparable to the ohmic loss at 1 GHz and the loss in PTFE is comparable to ohmic losses at 10 GHz. A low dielectric constant allows for a greater center conductor: less ohmic losses. An inhomogeneous dielectric needs to be compensated by a noncircular conductor to avoid current hot-spots.

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