Linear Time Calculation of On-Chip Power Distribution Network Capacitance Considering State-Dependence

A fast calculation tool for state-dependent capacitance of power distribution network is proposed. The proposed method achieves linear time-complexity, which can be more than four orders magnitude faster than a conventional SPICE-based capacitance calculation. Large circuits that have been unanalyzable with the conventional method become analyzable for more comprehensive exploration of capacitance variation. The capacitance obtained with the proposed method agrees SPICE-based method completely (up to 5 digits), and time-linearity is confirmed through numerical experiments on various circuits. The maximum and minimum capacitances are also calculated using average and variance estimation. Calculation times are linear time-complexity, too. The proposed tool facilitates to build an accurate macro model of an LSI. key words: capacitance, power distribution network, state-dependency, integrated circuit modeling, electromagnetic interference