1. Day 21: October 26, 2012 Distributed RC Delay
ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems
Day 21: October 26, 2012
Distributed RC Delay
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2. Today Estimate delay in RC Network Wire Delay Elmore delay calculation
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3. What is response?
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4. What is response?
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5. What is response?
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6. SPICE Response
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7. What is response?
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8. SPICE Response
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9. Intuition Look at series of R’s on path
Must move Q=V(SC) across each R
Not as much as if both R’s precede C’s
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10. Elmore Delay For each resistor Ri in path
Compute CRi = sum of all C’s downstream of Ri
Delay through Ri is Ri×CRi
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11. Superposition
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12. Superposition R1 R2 R1 C1 C2 R2 R1 C2 C1
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13. Superposition R1*C1 (R1+R2)*C2 R1 R2 R1 C1 C2 R2 R1 C2 C1
R1*(C1+C2)+R2*C2
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14. Superposition not concurrent
Don’t happen concurrently since must divide current
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15. Superposition For R1=R2=R, C1=C2=C Delay = 3RC R2 R1 C2 C1
R1*(C1+C2)+R2*C2
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16. SPICE Response
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17. Apply to Y
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18. Apply Y
1000W×3pF
+1000W×1pF
=4ns
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19. SPICE Response
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20. Elmore Delay For each resistor Ri in path
Compute CRi = sum of all C’s downstream of Ri
Delay through Ri is Ri×CRi
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21. Wire
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22. Wire Capacitance
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23. Wire Resistance
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24. Wire as RC Ladder
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25. Wire Delay as f(L) Measure wire length in units Say l
Each lambda have Cunit, Runit
Capacitance and resistance of wire of length l
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26. Wire Delay Delay of Wire N units long: Runit*(N*Cunit)
+Runit*Cunit
=(Runit*Cunit)*(N+N-1+N-2+….1)
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27. Sum of integers What’s the sum of the integer 1 to N? N+N-1+N-2+…1
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28. Sum of integers What’s the sum of the integer 1 to N? N+N-1+N-2+…1
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29. Wire Delay Wire N units long:
Runit*(N*Cunit)+Runit((N-1)*Cunit +Runit*(N-2)*Cunit+…+Runit*Cunit
=(Runit*Cunit)*(N+N-1+N-2+….1)
=Runit*Cunit*N2/2
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30. Wire Delay Rwire = N*Runit Cwire=N*Cunit Wire delay = Runit*Cunit*N2/2
Wire delay = 0.5 * Rwire*Cwire
Half the delay of lumped RC product
Quadratic in length of wire
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31. Wire Delay Wire N units long: With =Runit*Cunit*N2/2 Runit=1000W
Cunit=1pF
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32. RC Ladder
Runit=1000W
Cunit=1pF
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33. Animation
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34. Branching Wire What is delay of: L/2 Drive Receive L/2 L/2
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35. Branching Wire Drive Wire of length L
L2/2 (Runit*Cunit)
Charge L/2 Cunit through R=L/2 Runit
L2/4 (Runit*Cunit)
Total 0.75 L2
L/2
Drive
Receive
L/2
L/2
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36. Branching Wire Direct calc like ladder for first half
Then wire of length L/2
0.5(L/2)2=L2/8
Total 0.75 L2
L/2
Drive
Receive
L/2
L/2
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37. Idea Lumped wiring calculation is pessimistic
Not all capacitance at end of wire
Elmore delay calculation allows us to estimate
Wires are distributed RC
Half delay lumped calculation
Still quadratic in length
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38. Admin Project Try to turn around Milestone feedback today
Due next Thursday
Dig in ASAP
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