Performance Analysis (Clock Signal) مرتضي صاحب الزماني

Unbalanced delays Logic with unbalanced delays leads to inefficient use of logic: short clock period long clock period مرتضي صاحب الزماني

Flip-flop-based system performance analysis مرتضي صاحب الزماني

Flip-flop-based system model Clock signal is perfect (no rise/fall), period P. Clock event on rising edge. Setup time s. Time from arrival of combinational logic event to clock event. Propagation time p. Time for value to go from flip-flop input to output. Worst-case combinational delay C. Time from output of flip-flop to input. مرتضي صاحب الزماني

Clock parameters مرتضي صاحب الزماني

Clock period constraint P >= p + C + s. s C مرتضي صاحب الزماني

Clock with rise/fall tr is large because the clock wire is long and has high capacitance. مرتضي صاحب الزماني

Rise/fall clock period constraint P >= tr + p + C + s s tr C مرتضي صاحب الزماني

Skew Skew: relative delay between events. Clock skew: can harm any sequential system. مرتضي صاحب الزماني

Clock skew Clock must arrive at all memory elements in time to load data. مرتضي صاحب الزماني

Clock skew in system D Q logic d D Q مرتضي صاحب الزماني

Clock skew analysis model s12 = d1 – d2 Assume d1 > d2 (s12 > 0) φ مرتضي صاحب الزماني

Skew and clock period tsu= tr = 0 If clock arrives at FF1 after FF2, then there is less time for the signal to propagate through the combinational logic. Given clock period, determine allowable skew: P >= D2 + s12 مرتضي صاحب الزماني

Clock distribution Often one of the hardest problems in clock design. Fast edges. Minimum skew. مرتضي صاحب الزماني

Clock skew example 10 ps 10 ps 20 ps 20 ps 30 ps 30 ps D Q D Q 10 ps 10 ps 20 ps 20 ps 30 ps 30 ps مرتضي صاحب الزماني

Clock Skew مرتضي صاحب الزماني

Clock Routing Problem مرتضي صاحب الزماني

H-Tree Based Algorithm 16 points 4 points مرتضي صاحب الزماني

MMM Algorithm - Jackson, Srinivasan and Kuh, DAC 1990. مرتضي صاحب الزماني

MMM Steps مرتضي صاحب الزماني

Geometric Matching Algorithm مرتضي صاحب الزماني

Geometric Matching Algorithm مرتضي صاحب الزماني

Weighted Center-Based Algorithm مرتضي صاحب الزماني

Weighted Center-Based Algorithm × Tapping Point Selection مرتضي صاحب الزماني

Observation Do we really need to make the skew zero for all flip-flops? Not many clean and/or optimal techniques work in this less constrained regime Y. Chen, A.B. Kahng, G. Qu,A. Zelikovsky, “The Associative Clock Routing Problem,” ACM/ IEEE Design Automation Conference, 1999. مرتضي صاحب الزماني