Modified Rational Function Modeling Technique for High Speed Circuits

This paper presents a modified rational function modeling technique for high speed circuits. It models the scattering parameters (S-parameters) of high speed circuits with modified rational functions. S-parameters can be directly measured or simulated using traditional circuit simulation tools, and the poles and residues of modified rational functions are determined by a vector fitting algorithm. Compared to the traditional rational functions, far fewer poles are needed. With the modified rational functions, the time-domain-reflectometry, time-domain-transmission waveforms and output signals of high speed circuits can be easily expressed in closed-forms, providing a simple way to do quasi-analytic time domain analysis of measured microwave structures. The presented modeling technique is demonstrated for a differential transmission channel on a high-speed electrical backplane