1. Day 24: October 28, 2013 Distributed RC Wire and Elmore Delay
ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems
Day 24: October 28, 2013
Distributed RC Wire and
Elmore Delay
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2. Previously: Equivalent RC
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3. Previously: Chain without Inverters
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4. Today Estimate delay in RC Network Wire Delay Elmore delay calculation
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5. Distributed RC
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6. What is response?
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7. SPICE Response
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8. 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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9. 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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10. Superposition
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11. Superposition R1 R2 R1 C1 C2 R2 R1 C2 C1
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12. Superposition R1*C1 (R1+R2)*C2 R1 R2 R1 C1 C2 R2 R1 C2 C1
R1*(C1+C2)+R2*C2
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13. Superposition not concurrent
Don’t happen concurrently since must divide current
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14. Superposition For R1=R2=R, C1=C2=C Delay = 3RC R2 R1 C2 C1
R1*(C1+C2)+R2*C2
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15. SPICE Response
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16. Apply to Y
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17. Apply Y
1000W×3pF
+1000W×1pF
=4ns
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18. SPICE Response
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19. 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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20. Wire
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21. Wire Capacitance
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22. Wire Resistance
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23. Wire as RC Ladder
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24. 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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25. 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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26. Sum of integers What’s the sum of the integer 1 to N? 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. 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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29. 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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30. Wire Delay Wire N units long: With =Runit*Cunit*N2/2 Runit=1000W
Cunit=1pF
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31. RC Ladder
Runit=1000W
Cunit=1pF
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32. Animation
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33. Apply to Pass Transistor (and CMOS)
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34. Pass TR xor
Delay when B=1?
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35. Pass transistor xor Delay when B=0? Start with RC
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36. Unbuffered
Circuit  Delay?
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37. Unbuffered
Circuit  Delay?
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38. Unbuffered Delay as a function of number of stages?
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39. CMOS xor
Delay with Cdiff>0?
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40. 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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41. Admin Project André no office hours Tuesday
Should have feedback from preclass on canvas
Due Thursday
André no office hours Tuesday
2nd midterm next Monday (11/4)
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