Optimal spacing and capacitance padding for general clock structures

Authors:
Yu-Min Lee;Hing Yin Lai;Charlie Chung-Ping Chen
Affiliations:
Department of Electrical and Computer Engineering, University of Wisconsin at Madison, Madison, WI;Department of Electrical and Computer Engineering, University of Wisconsin at Madison, Madison, WI;Department of Electrical and Computer Engineering, University of Wisconsin at Madison, Madison, WI
Venue:
Proceedings of the 2001 Asia and South Pacific Design Automation Conference
Year:
2001

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Abstract

Clock-tuning has been classified as important but tough tasks due to the non-convex nature caused by the skew requirements. As a result, all existing mathematical programming approaches are often trapped at local minimum and have no guarantee of obtaining global optimal solution. In this paper, we present optimal clock tuning algorithms which effectively apply capacitance-padding to reduce clock skew, power, and delay for general clock topologies. Capacitance-padding can be achieved by wire-spacing, wire-splitting, wire-padding and transistor-padding. We show that under the El-more delay model, capacitance-padding can be formulated as a linear programming problem and solved with great efficiency. Capacitance-padding can also be used as a post processing step for any non-zero-skew clock tree or mesh structure to achieve timing closure. Experiment results on several practical industry examples show that our algorithms are extremely efficient. Problems with over 6000 variables can be optimally tuned within 1 minute on a PC with 500 -MHZ Intel Pentium III processor.