1. Performance Analysis
(Clock Signal)
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2. Unbalanced delays
Logic with unbalanced delays leads to inefficient use of logic:
short clock period
long clock period
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3. Flip-flop-based system performance analysis
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4. 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.
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5. Clock parameters
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6. Clock period constraint
P >= p + C + s. s C
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7. Clock with rise/fall
tr is large because the clock wire is long and has high capacitance.
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8. Rise/fall clock period constraint
P >= tr + p + C + s s tr C
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9. Skew Skew: relative delay between events.
Clock skew: can harm any sequential system.
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10. Clock skew
Clock must arrive at all memory elements in time to load data.
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11. Clock skew in system D Q
logic d D Q
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12. Clock skew analysis model
s12 = d1 – d2
Assume d1 > d2 (s12 > 0) φ
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13. 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
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14. Clock distribution Often one of the hardest problems in clock design.
Fast edges.
Minimum skew.
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15. Clock skew example 10 ps 10 ps 20 ps 20 ps 30 ps 30 psD Q D Q
10 ps
10 ps
20 ps
20 ps
30 ps
30 ps
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16. Clock Skew
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17. Clock Routing Problem
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18. H-Tree Based Algorithm
16 points
4 points
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19. MMM Algorithm - Jackson, Srinivasan and Kuh, DAC 1990.
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20. MMM Steps
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21. Geometric Matching Algorithm
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22. Geometric Matching Algorithm
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23. Weighted Center-Based Algorithm
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24. Weighted Center-Based Algorithm×
Tapping Point Selection
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25. 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.
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