Estimation of proximity effect on the electrical characteristics of multi-conductor lines

Investigations on the effect of non-uniformity in charge distribution over the surfaces of parallel cylinders of transmission lines due to the proximity effect on their impedance and field distribution are presented. Expressions for the location of points which are mutually inverse to a pair of circles representing the cross-sections of parallel cylinders and through which the equivalent filamentary line charges pass are first found. The potential function, capacitance, impedance and field distribution for a line consisting of a centre cylinder surrounded by a number of grounded cylinders are found in terms of the expressions for the inverse points. Numerical data are presented for: a two-conductor line of unequal radius; a three-conductor line with coplanar axes and symmetric as well as asymmetric location of grounded conductors; a four-conductor line with non-coplanar axes and finally, a multi-conductor line.