In today's highly competitive IC marketplace, company survival necessitates product differentiability. Product differentiability may be engendered in many ways, several of which include: increased performance (e.g. lower power, faster timing, etc...), lower cost, more features, or faster time to market. Thus, the motivation for design techniques that enhance chip timing performance are of fundamental importance to the IC community. The clock is the essence of a synchronous digital system. Physically, the clock is distributed from an external pad to all similarly clocked synchronizing elements through a distribution network that encompasses combinational logic and interconnects. It serves to unify the physical and temporal design abstractions by determining the precise instants in time at which the digital machine changes state. Because the clock is important, optimization of the clock signal can have a significant impact on the chip's cycle time, especially in high-performance designs. Non-optimal clock behavior is caused by two phenomena: the routing to the chip's synchronizing elements, and the asymmetric behavior of the clock distribution logic. Previous work in clock optimization has been contributed by several authors. H-trees have been recognized for years as a technique to help reduce the skew in synchronous systems [FK82] [KGE82] [DFW84] [BWM86]. For regular structures such as systolic arrays the H-tree works well to reduce skew because the synchronizing elements are distributed in a uniform pattern throughout the chip. However, for general design styles, nonuniform distributions of clock pins are common and the H-tree becomes ineffective as a technique for clock routing. The large size of the clock net has led some researchers [DFW84] [Mij87] to perform buffer optimization within the clock distribution tree. [BWM86] have provided an analysis of the clock tree that considers the transmission line properties of the interconnects. [BBB +89] have presented an approach for ASIC clock distribution that integrates buffer optimization into place and route algorithms. However, in all previous work the routing of the clock net is performed using ordinary global routing tools based on minimum spanning or approximate minimum Steiner tree net models and with detailed routers that have little understanding of clock routing problems. This causes non-optimal clock behavior and as region size or the number of pins in the clock net increases, the detrimental behavior is exacerbated. In this paper, we focus on routing techniques for optimizing clock signals in VLSI circuits. We demonstrate the superiority of our algorithm over standard routing techniques for widely varying region size, clock pin distributions, numbers of clock pins and technology feature size. In section two the preliminaries necessary for understanding the paper are presented. Following this, in section three the problem is defined. Section four illustrates the algorithm for clock routing and section five discusses theoretical results. Next, in section six the experimental results are presented, and in section seven possible avenues for future work and conclusions regarding the approach are discussed.




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