Transmission-line Parameters

Author: Edmund A. Laport

The fundamental electrical characteristics are derived from the configuration of the electric and magnetic fields surrounding the conductors, which in turn are derived from the parameters of the cross-sectional geometry of the line and the nature of the enclosing dielectric medium. In the quasi-static case, corresponding to typical engineering usage, the transmission lines under consideration propagate transverse electromagnetic waves (waves in which the electric and magnetic vectors are mutually normal and also normal to the direction of propagation), but the parameters are derivable from electrostatics or magnetostatics. The electrostatic solution, using the theory of logarithmic potentials, is most convenient for the purpose when no ferromagnetic effects are involved. The solution, starting with scalar potentials and charges, yields the unit-length capacitance, characteristic impedance, charge distributions, and velocity of propagation (for example, see Chap. 6). The equipotential surfaces and potential gradients can be calculated from the same information.

An alternative method is that from magnetostatics, using the system of logarithmic vector potentials and currents. The solutions also yield the unit-length inductance, characteristic impedance, current distributions, and the velocity of propagation.

The unit-length resistance and leakance are empirical and depend upon the number of wires and their resistivity, the frequency, the current distribution in the wires, the method and material of insulation, and the conductivity of the soil under the line (when ground-return currents are present). Any concentrated dielectric or ferromagnetic materials in the field of the line can also influence the fundamental parameters to some extent, but ideally they are assumed not to exist. In practice, care is taken to minimize their presence. When the line conductors are of permeable material, the permeability acts with the conductivity as a factor in increasing skin effect and thus increasing the high-frequency resistance.