Frequency-domain solution for coupled striplines with crossing strips

A frequency-domain approach to the modelling of the propagation of short-rise-time digital pulses along groups of coupled striplines, which are overcrossed or undercrossed by orthogonally positioned signal conductors on adjacent signal planes in a high-density circuit board or multichip module substrate is presented. A solution is presented which has several particular features which are important in the application of this method to real-world modeling problems. The solution significantly simplifies the mathematical formulas which sum the multiple reflections and crosstalk components with the primary digital pulse to generate the final waveform conformations on the multiple conductors. As a result, this method is much easier to implement than earlier techniques, especially as a software kernel for a computer-aided design tool. The method presented reduces the central processing unit time needed to execute these solutions by a nontrivial factor of 2-3 in comparison with a previously published method. The method removes the earlier constraint that the crossing strips on the orthogonal signal layer be uniformly spaced: that is, nonuniformly spaced crossing strips are supported by the mathematical derivation. The derivation allows for nonideal voltage sources