Electrostatic field of coplanar lines computed with the point matching method

A computational method for calculating the electric potential generated by a set of electrodes on top of a layered dielectric medium is described. The potential function is expressed by series expansions in terms of solutions of the Laplace equation. One such expansion is written down for each homogeneous region of the layered structure. The structure coefficients of the different series are related to each other and to the potentials applied to the electrodes via boundary conditions. In the plane of the electrodes, the boundary conditions are satisfied at N discrete points with N being equal to the number of terms in the series expansions. The resulting system of inhomogeneous equations is solved by matrix inversion with the help of a personal computer.