Scattering matrix approach for frequency and time domain crosstalk analysis in multilayer PCBs

The problem of crosstalk evaluation among PCB traces in a multilayer structure is studied by means of an S-matrix technique. Two bundles of parallel lines, perpendicularly crossing on different layers, are analysed, and this complex structure is decomposed into subsystems, each of them characterised by its S matrix. The elementary subsystems consist of bundles of parallel lines and crosses of two lines. A particular algorithm, developed to number the ports of each subsystem, allows one to easily recognise the interconnected ports and the external ports (I/O ports), to achieve the S matrix of the overall structure in terms of the I/O ports. The application of this technique to a 3×3 and a 7×7 configuration shows a good agreement between theoretical and experimental results. Finally, the analysis in the frequency domain is extended to the time domain by a standard FFT algorithm, and, as an example, an ESD current flowing along a line is examined, as well as its coupling toward an adjacent and crossing line.