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

The analysis of electromagnetic propagation over uniform cables depends on the calculation of the charge densities on the conductors, relative to a potential function that is not necessarily constant on the conductors. By considering such a potential function as the real part of an analytic function, two Laurent series are derived, one of which involves the Fourier components of the potential function and its associated charge densities on the conductors. The second series accounts for the relative location of the conductors. The two series are equated to give a system of linear equations that can be solved for the charge components. The results obtained, which apply to uniform cables whose conductors (including the shield, if present) have circular cross sections and are covered with two layers of dielectric insulation, can be used to calculate the propagation modes and propagation constants of the cable.