Maximum voltage variation in the power distribution network of VLSI circuits with RLC models

In this paper, we present a frequency-domain technique to estimate the worst-case time-domain voltage variation using RLC models for the power distribution network. The proposed method, unlike existing simulation-based techniques, can handle frequency-dependent RLC parameters and generate an upperbound on the maximum voltage drop over all possible input excitations. Pattern independent maximum envelope currents are used to estimate the upperbound on the maximum magnitude of the frequency components for the current waveform. These values are used to formulate a nonlinear optimization problem for the maximum voltage drop at nodes in the power distribution network. We then present a method to solve the nonlinear optimization problem using Lagrange multipliers. Comparisons with SPICE simulations are presented to validate the techniques presented in the paper.