The Theory of Uniform Cables - Part II: Calculation of Charge Components

Multiconductor cables for telecommunications have distributions of charge on each conductor. The surface charge density on the conductors is proportional to the normal derivative of a potential function (i.e., a solution to Laplace's equation), which is defined in the region separating the conductors and is constant on the conductors. The constant values of the potential are the voltages of the conductors, and the proportionality constant is the permittivity of the material next to the conductor. Also, generalized charge densities are defined for potential functions, such as the longitudinal component of the electric field, which are not constant on the conductors. In the present work an algorithm is developed for computing the charge densities in this generalized sense for uniform cables. Thus, the conductors of the cable are assumed to be straight and parallel, so that each transverse cross section is identical. The wires are assumed to have 611 Fig. 1--Typical cable cross section circular cross sections and to be covered by two circularly symmetric layers of homogeneous dielectric material. Surrounding the collection of wires is a circular, metallic shield, and it too is assumed to have two uniform layers of dielectric on its inside surface. A typical cross section is shown in Fig. 1. Interest in the charge densities was spurred by the recent finding that the modes of a cable and their associated propagation constants can be expressed directly in terms of the charge densities when, as in Kuznetsov's work,1 low frequencies are excluded.