Finite-difference computation of the characteristic impedance of unbounded striplines and microstrip lines

A novel numerical method for the computation of the TEM characteristic impedance of unbounded striplines and microstrip lines is presented. The method uses non-linear orthogonal transformations to map the unbounded domain into a rectangle for the application of the finite-difference method. Equations for the electrostatic potential and the per-unit length capacitances are derived in the transformed domain. The finite-difference method is applied to obtain discrete versions of these equations. The over-relaxation algorithm is used to solve the discrete equations for the electrostatic potential. The characteristic impedance is computed in terms of the per-unit length capacitances. The implementation of the algorithm that solves the discrete equations is described. Results computed with our method and with Wheeler´s formulas are compared, showing excellent agreement between the two methods