Buffers in clock trees introduce two additional sources of skew: the first source of skew is the effect of process variations on buffer delays. The second source of skew is the imbalance in buffer loading. We propose a buffered clock tree synthesis methodology whereby we first apply a clustering algorithm to obtain clusters of approximately equal capacitance loading. We drive each of these clusters with identical buffers. A sensitivity based approach is then used for equalizing the Elmore delay from the buffer output to all of the clock nodes. The skew due to load imbalance is minimized concurrently by matching a higher-order model of the load by wire sizing and wire lengthening. We demonstrate how this algorithm can be used recursively to generate low-skew buffered clock trees.

In this paper, we consider non-uniform wire-sizing.Given a wire s e gment of length L, let f(x) be the width of the wire at position x, 0 x L .We show that the optimal wiresizing function that minimizes the Elmore delay through the wire i s f ( x ) = ae bx , where a > 0 and b > 0 are c onstants that can be c omputed i n O (1) time.In the case where lower bound (L > 0 ) and upper bound (U > 0 ) on the wire widths are given, we show that the optimal wire-sizing function f(x) is a truncated version of ae bx that can also be determined i n O (1) time.Our wire-sizing formula can be iteratively applied to optimally size the wire s e gments in a routing tree.

We consider the problem of minimizing the number of logic modules for Actel 2 or Actel 3 sequential circuits. We make use of the fact that if a flip-flop is the only destination of its driving combinational block, then both the flip-flop and the combinational block can be put in a sequential module. Retiming technique is applied to minimize the number of resistors that can not be merged with combinational blocks. We formulate the problem as an integer linear program. We show that the constraint matrix of the integer program is totally unimodular. As a result, we can solve our logic module minimization problem optimally by solving the linear relaxation of the integer program.>