Evaluation of capacitance matrix of a finite-length multiconductor transmission line

A method for the evaluation of the capacitance matrix of a system of finite-length conductors is given. It is shown that the problem can be reduced to the solution of a convolution-type integrodifferential equation system and an effective and accurate procedure to cope with this is described. The procedure first applies the convolution theorem to the initial integrodifferential equation system to obtain an algebraic one in terms of the Fourier coefficient of the original unknown function. Next, this new system is diagonalised and reduced to a set of decoupled equations. These are then solved by means of an ad hoc developed algorithm, essentially based on a representation of the Fourier coefficient in terms of the Neumann series. The proposed approach is applied to a two-conductor test line and the obtained numerical results for different conductors radius values are compared with those provided by the classical infinite-length-conductor approximation.