Fast simulation method for the detection of reflection—and crosstalk effects during the design of complex printed circuit boards

In this paper two fast frequency domain methods are presented for the determination of the voltages at all terminations of coupled transmission line systems. Algorithms based on these methods can be used for a fast preanalysis of complex PCBs with respect to re ection{ and crosstalk e ects. The dynamical behaviour of a transmission line system is described by a frequency dependent transfer matrix which is calculated with two di erent methods. The rst method is based on a Pad e Approximation and the second requires the knowledge of the eigenvalues and the eigenvectors of the product of the inductance and capacitance matrix. Within both methods the symmetry of these matrices and a fundamental property of the matrix exponential were used to develop e cient algorithms.