Modified rational function modeling for multi-port high-speed differential circuits

This paper presents a modified rational function modeling technique for multi-port high-speed differential circuit simulations. It models the differential channel and multi- aggressor crosstalk with modified rational functions extracted from the single-ended multi-port S-parameters of the circuit. The multi-port S-parameters of a high-speed circuit can be directly measured or simulated using electromagnetic simulators, and the poles and residues of the modified rational functions are determined by a vector fitting algorithm. Compared to the traditional rational function modeling, far fewer poles are needed to model a channel and crosstalk. With the modified rational function modeling technique, the output signals of the differential channel and crosstalk can be expressed in closed forms, providing a simple way to do quasi-analytic time-domain analysis of multi-port differential structures. The presented modeling technique is demonstrated for a 16-port high-speed electrical backplane.