1. Day 23: November 3, 2010 Driving Large Capacitive Loads
ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems
Day 23: November 3, 2010
Driving Large Capacitive Loads
Penn ESE370 Fall DeHon

2. Today How do we drive a large load? Stages and buffer sizing
Minimum delay
Penn ESE370 Fall DeHon

3. Start Cdiff=0
Penn ESE370 Fall DeHon

4. One Stage
How size to minimize delay?
Penn ESE370 Fall DeHon

5. One Stage
Delay equation?
Penn ESE370 Fall DeHon

6. Minimize Differentiate and set to zero. What’s WN?
Penn ESE370 Fall DeHon

7. Solving for size
Penn ESE370 Fall DeHon

8. N-stage
Penn ESE370 Fall DeHon

9. N-stage Delay
Penn ESE370 Fall DeHon

10. Size WNi to minimize delay
Take partial derivative wrt WNi
Penn ESE370 Fall DeHon

11. Solving for WNi
Penn ESE370 Fall DeHon

12. Delay
Penn ESE370 Fall DeHon

13. Stage Delay
Penn ESE370 Fall DeHon

14. Stage Delay
Penn ESE370 Fall DeHon

15. Stage Delay
Penn ESE370 Fall DeHon

16. Total Delay
Penn ESE370 Fall DeHon

17. Minimize
Penn ESE370 Fall DeHon

18. Solve
Penn ESE370 Fall DeHon

19. Optimum Scale Up
Penn ESE370 Fall DeHon

20. Delay at Optimum
Penn ESE370 Fall DeHon

21. Cdiff=gCgate
Penn ESE370 Fall DeHon

22. N-stage Delay
Penn ESE370 Fall DeHon

23. N-stage Delay
Penn ESE370 Fall DeHon

24. Impact on Min Wni ? Partial Derivative unchanged
Penn ESE370 Fall DeHon

25. Total Delay
Penn ESE370 Fall DeHon

26. Stage Delay: N=7
N+1=8
Penn ESE370 Fall DeHon

27. Stage Delay, g=0.5
N+1=8
Penn ESE370 Fall DeHon

28. Stage Delay: N=6, g=0.5
N+1=7
Penn ESE370 Fall DeHon

29. Stage Delay: N=5, g=0.5
N+1=6
Penn ESE370 Fall DeHon

30. Stage Delay: N=4, g=0.5
N+1=5
Penn ESE370 Fall DeHon

31. Optimal Staging g≠0
Penn ESE370 Fall DeHon

32. Admin
Friday
Lecture
HW5 due
Proj2 out
Penn ESE370 Fall DeHon

33. Idea Drive large loads with geometrically sized buffer chain
There is an optimal buffer ratio
Technology/gate dependent
Depends on self-loading
Penn ESE370 Fall DeHon