Electromagnetic characterization of shielded multiconductor microstrip-line discontinuities using the time-domain finite-difference method

The time-domain finite difference (TD-FD) method is applied to obtain the frequency-dependent characteristics of shielded multiconductor microstrip line interconnect structures. A Gaussian pulse is used as the excitation source and the reflected, transmitted, and coupled pulses on the various lines are used for the calculation of the frequency-dependent elements in the scattering matrix representation of the structure. In order to correctly specify the frequency range of applicability of the results, the cutoff frequencies of the higher-order modes of the structures under consideration need to be found. This is done by a two-dimensional application of the TD-FD method over the cross-section of the multiconductor transmission line, based on the simple observation that modes at cutoff are characterized by the fact that ∂/∂z = 0 where z is the direction of propagation along the axis of the line. Numerical results are obtained for the dispersive characteristics of coupled microstrip lines and the frequency-dependent scattering parameters of a microstrip open-end line, a 90° bend, a right-angle via, and the discontinuity which occurs when one of the two lines is terminated in a coupled symmetric microstrip geometry