Fast simulation of reflection and crosstalk effects using a Pade approximation

The detection of reflection- and crosstalk-effects during the design of complex printed circuit boards is very time consuming if it is based on an accurate simulation of the voltages at the inputs and outputs of all transmission lines. A division of the complete analysis process into a fast and approximative preanalysis and the following accurate simulation of those nets, which have been classified to be probably critical, can speed up the whole procedure. In the paper a fast method for the determination of the voltages at all terminations of coupled transmission line systems is presented. It is working in the frequency domain and it can be used for a fast preanalysis of complex PCBs with respect to reflection and crosstalk effects. The dynamic behaviour of a transmission line system is described by a frequency dependent transfer matrix, which is calculated with a Pade approximation. Therefore, the calculation of the eigenvalues and eigenvectors of the system is not necessary. The symmetry of the inductance and capacitance matrices of the transmission line system and a fundamental property of the matrix exponential are used to develop and implement an efficient algorithm