Method of moments capacitance model for multiconductor systems

Abstract

Industry would like an analytical model that can predict various electrical parameters to characterize the performance of their components rather than building prototypes and testing. Of importance are parameters such as capacitive loading effects, inductance, delay characteristics, characteristic impedance, signal bandwidth and distortion, system stability, radiated emissions, passive filtering, and crosstalk (electromagnetic coupling). These parameters need to be evaluated for various geometries such as multiconductor ribbon cables, wire bundles, coax cables, shielded wire bundles, twisted pairs, and wire bundles over a ground plane. Also of importance is how to handle all of the above conditions with discontinuities in geometry. The primary objective of this discussion is to develop a mathematical model which will determine the capacitance of various multiconductor systems, the model being a FORTRAN program. It can be shown that once the capacitance is known all other parameters can be obtained. The capacitance model developed in this document uses a Fourier series approximation for the charge density on the conductor and dielectric surface. Using the charge density described above a near field potential function is developed for cylindrical conductors. The potential function is descritized and placed in matrix form using the "method of moments," which was first introduced by R. F. Harrington. When the wires are coated with a dielectric it is necessary to determine the electric field intensity. The electric field intensity is needed to completely specify or determine all the unknown charge densities on the conductor and dielectric surfaces. This is accomplished by using the potential function developed above and using Laplace's equation. The capacitance matrix models which are presented in this document include dielectric coated multiconductor ribbon cables, dielectric coated multiconductor wire bundles with different radii and permittivities, shielded multiconductor wire bundles, multiconductor coax cables, and dielectric coated multiconductor wire bundles over a ground plane. This report contains a discussion of the theory for the determination of the capacitance for the various configurations discussed above as well as some of the anomalies associated with various models and the FORTRAN program itself. Wherever possible, comparison of the capacitance model using the method of moments is made ot that of the closed form solution, specifically, that of an uncoated (bare) 2-wire system, coax cable, shielded wire, and one bare wire over a ground plane. When discussing the capacitance o dielectric coated wires and those over a ground plane, the model is compared with results that are obtained from testing.