An algorithm has been developed for the automatic determination of the optimal clock waveforms for synchronous circuits containing level-sensitive latches. From a specification of only the number of clock phases, the rise and fall times of the clock phase transitions, and the order in which they occur, the algorithm computes the minimum time interval between the transitions, while accounting for the clock skew. Timing errors, such as incorrect hold times, are also detected. Existing procedures, in contrast, either verify if a circuit meets a given specification of these clock intervals, or they work with a very restricted set of clocking schemes. The procedure is iterative, and can be formulated as a linear programming problem. It yields an upper bound on the shortest valid clock period at each iteration. Results are presented for a simplified form of this algorithm, implemented in the transistor-level timing analysis program TAMIA.
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