1. Penn ESE370 Fall2010 -- DeHon 1 ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 7: September 22, 2010 Delay and RC Response

2. Delay is RC Charging Penn ESE370 Fall2010 -- DeHon 2

3. Delay is RC Charging Understand switch state Break into stages For each stage –Understand R drive –Understand C load Penn ESE370 Fall2010 -- DeHon 3

4. Today RC Charging RC Step Response What is the C? What is the R? Measuring Delay Delay model of gate Penn ESE370 Fall2010 -- DeHon 4

5. 90% Rise Time? Penn ESE370 Fall2010 -- DeHon 5

6. What does response look like? Penn ESE370 Fall2010 -- DeHon 6

7. What does look like? Penn ESE370 Fall2010 -- DeHon 7

8. Shape of Curve x e -x 1-e -x 0 0.1 1 2 2.3 Penn ESE370 Fall2010 -- DeHon 8

9. Shape of Curve x e -x 1-e -x 010 0.10.90.1 11/e = 0.370.66 21/e 2 = 0.140.86 2.30.10.9 Penn ESE370 Fall2010 -- DeHon 9

10. What is C? Penn ESE370 Fall2010 -- DeHon 10

11. Capacitance Wire MOSFET gate Logical Gate Fanout -- Total gate load Penn ESE370 Fall2010 -- DeHon 11

12. Wire Capacitance Penn ESE370 Fall2010 -- DeHon 12

13. Wire Capacitance Penn ESE370 Fall2010 -- DeHon 13

14. There are always Rs and Cs Modeling vs. discrete components Dominant effects –Rbig + Rsmall ≈ Rbig –Cbig || Csmall ≈ Cbig Penn ESE370 Fall2010 -- DeHon 14

15. First Order Model Switch –Loads input capacitively As dig in, understand: –Origin of capacitance –How can we engineer –Tradeoffs Penn ESE370 Fall2010 -- DeHon 15

16. Logic Gate Input Capacitance Capacitance on –A input? –B input? Penn ESE370 Fall2010 -- DeHon 16

17. Fanout in Circuit Output routed to many gate inputs Penn ESE370 Fall2010 -- DeHon 17

18. Fanout in Circuit Maximum fanout? Second? Min? Penn ESE370 Fall2010 -- DeHon 18

19. Lumped Capacitive Load Penn ESE370 Fall2010 -- DeHon 19

20. What is R? Penn ESE370 Fall2010 -- DeHon 20

21. Resistance Wire resistance –Supply to transistor source –Transistor output gate it is driving Transistor equivalent resistance Penn ESE370 Fall2010 -- DeHon 21

22. Wire Resistances Penn ESE370 Fall2010 -- DeHon 22

23. First Order Model Switch –Resistive driver As dig in, understand: –More sophisticated view –How can we engineer –Tradeoffs Penn ESE370 Fall2010 -- DeHon 23

24. Equivalent Resistance What resistances might transistors contribute? –How many cases? Penn ESE370 Fall2010 -- DeHon 24

25. Lumped Resistive Source Penn ESE370 Fall2010 -- DeHon 25 R trnet = parallel and series combination of R tr

26. Measuring Delay Penn ESE370 Fall2010 -- DeHon 26

27. Measuring Gate Delay Next stage starts to switch before first finishes Measure 50%--50% Penn ESE370 Fall2010 -- DeHon 27 67ps 80ps

28. Characterizing Gate/Technology Delay measure will be –Function of load on gate –Function of input rise time Which, in turn, may be a function of input loading Penn ESE370 Fall2010 -- DeHon 28

29. Delay vs. Risetime Penn ESE370 Fall2010 -- DeHon 29 10ps delay 20ps delay 1ps rise100ps rise

30. Characterizing Gate/Technology Delay measure will be –Function of load on gate –Function of input rise time Which, in turn, may be a function of input loading Want to understand typical –At least comparable Penn ESE370 Fall2010 -- DeHon 30

31. Measuring/Characterizing Drive with a gate –Not an ideal source Measure loaded gate –Typical loading – FO4 Penn ESE370 Fall2010 -- DeHon 31

32. HW2 Recommendation Penn ESE370 Fall2010 -- DeHon 32

33. Rise/Fall Rise and Fall time may differ –Why? Penn ESE370 Fall2010 -- DeHon 33

34. Delay Model of Gate Penn ESE370 Fall2010 -- DeHon 34

35. Sample Gate Penn ESE370 Fall2010 -- DeHon 35

36. Sample Gate Internal stages have delay External depend on load Assume (guarantee) all inputs same load Penn ESE370 Fall2010 -- DeHon 36

37. Sample Gate What is A? B? Penn ESE370 Fall2010 -- DeHon 37

38. Admin HW1 grades posted HW2 due Friday Here on Friday for lecture Penn ESE370 Fall2010 -- DeHon 38

39. Delay is RC Charging Penn ESE370 Fall2010 -- DeHon 39