Modeling and analyzing power integrity using GTLE and FDFD

This paper presents a numerical approach that combines the 2D Generalized Transmission Line Equations (GTLE) method and finite difference frequency-domain (FDFD) method to model and analyze the two-dimensional electromagnetic problem concerned in the power integrity (PI), which is becoming increasingly worse with the increase in clock frequency and density of the switching circuits, and with the decrease in supply-voltage levels. In this work, we use the 2D GTLE to model the power/ground planes pair. By this, a numerical method using circuit analysis can be developed for the analysis of a power/ground plane pair which can be equivalent to some distributed RLCG elements. Then,the FDFD is used to develop a simple algorithm to analyze 2D GTLE. By incorporating the GTLE and FDFD, we can find the resonant frequencies of power planes and calculate the Z-/S- parameters for selected circuit ports. Furthermore, by this approach, we can model the power/ground plane with surface mounted passive device, such as R, L, C and G. In this paper, the fringe effect (inner/ outer) is modeled by the virtual edge around the actual one which is efficient and easy to implement. The results from our method were compared to those from a full-wave simulator to show efficiency in power integrity simulation.