A perturbative approach to predict eye diagram degradation in differential interconnects subject to asymmetry and nonuniformity

This paper proposes a novel framework for the signal integrity (SI) analysis of differential interconnects affected by nonuniformity and geometrical asymmetry. The pertinent nonuniform transmission-line (TL) equations are solved in the frequency domain by means of a perturbation technique, which allows interpreting the resulting response degradation as a perturbation with respect to the response of a reference uniform differential line (DL) with averaged per-unit-length (p.u.l.) parameters. Following this interpretation, the problem is recast as a standard TL equation for the reference uniform line with additional equivalent distributed sources that account for the perturbative effect of asymmetric nonuniformity. This equivalent perturbation problem is solved iteratively in the frequency domain, and the corresponding time-domain behavior is obtained via inverse Fourier transform. Moreover, upon consideration that local perturbations negligibly impact on far-end differential mode (DM) quantities, the uniform DL model with averaged p.u.l. parameters is used for the SI performance evaluation of transmitted DM voltages in SPICE, showing that comparable results can be obtained while avoiding the cumbersome implementation of a nonuniform transmission line topology. The methodology is applied to the prediction of the eye diagram degradation for a 20 Gbps transmission through a microstrip DL subject to geometrical asymmetry and nonuniformity.