The Transverse Distribution of Surface Charge Densities on Multiconductor Transmission Lines

This paper is concerned with a problem which occasionally arises in the general area of multiconductor transmission line theory. In the past, the method of moments has been applied [1], [2] for the computation of transverse charge distribution and the capacitive-coefficient matrix for electrostatic systems formed by multiconductor transmission lines, with prescribed voltages on each line. But classically, there has been an interest in the related problem of finding the transverse charge distributions, given the net charge on each line [3], [4]. When the net charges are prescribed, conformalmapping techniques have been successfully employed in determining the charge distributions for certain special cases, e.g., the two-wire problem [5] and a planar grating [6]. The integral-equation formulation presented in this note for the charge distributions is applicable to a general system of parallel conductors, not necessarily in the same plane, as long as their net charges are prescribed. Another important application of this method lies in determining the field-coupling parameters when the multiconductor transmission line is illuminated by an external field.