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

TLDR: A fast calculation tool for state-dependent capacitance of power distribution network achieves linear time-complexity, which can be more than four orders magnitude faster than a conventional SPICE-based capacitance calculation.

Abstract: 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.

Figures

Fig. 2 On-chip capacitances.

Fig. 4 Proposed capacitance calculation flow.

Fig. 1 Linear equivalent circuit and current source (LECCS model) [1].

Fig. 11 Capacitance distribution of single DES IP core.

Fig. 10 Circuit capacitance calculation results comparison.

Fig. 3 Contribution of wire capacitances to the total capacitance.