ECEN
687Lec19_Interconnect.pdf

# 687Lec19_Interconnect.pdf - ECEN 687 VLSI Design Automation...

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ECEN 687 Lecture 19 1 ECEN 687 VLSI Design Automation Lecture 19 Interconnect Optimization

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2 R Buffers Reduce Wire Delay x/2 cx/4 cx/4 rx/2 t_unbuf = R( cx + C ) + rx( cx/2 + C ) t_buf = 2R( cx/2 + C ) + rx( cx/4 + C ) + t b t_buf – t_unbuf = RC + t b – rcx 2 /4 x/2 cx/4 cx/4 rx/2 C C R x t ECEN 687 Lecture 19
3 Buffers Improve Slack RAT = 300 Delay = 350 Slack = -50 RAT = 700 Delay = 600 Slack = 100 RAT = 300 Delay = 250 Slack = 50 RAT = 700 Delay = 400 Slack = 300 Slack min = -50 Slack min = 50 Decouple capacitive load from critical path RAT = Required Arrival time Slack = RAT - Delay ECEN 687 Lecture 19

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4 Problem Formulation Given n A Steiner tree n RAT at each sink n A buffer type n RC parameters n Candidate buffer locations Find buffer insertion solution such that the slack min is maximized ECEN 687 Lecture 19
5 Candidate Buffering Solutions ECEN 687 Lecture 19

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6 Candidate Solution Characteristics Each candidate solution is associated with n v i : a node n c i : downstream capacitance n q i : RAT v i is a sink c i is sink capacitance v is an internal node ECEN 687 Lecture 19
7 Van Ginneken s Algorithm •Start from sinks •Candidate solutions are generated Candidate solutions are propagated toward the source ECEN 687 Lecture 19

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8 Solution Propagation: Add Wire c 2 = c 1 + cx q 2 = q 1 – rcx 2 /2 – rxc 1 r: wire resistance per unit length c: wire capacitance per unit length (v 1 , c 1 , q 1 ) (v 2 , c 2 , q 2 ) x ECEN 687 Lecture 19
9 Solution Propagation: Insert Buffer n c 1b = C b n q 1b = q 1 – R b c 1 – t b n C b : buffer input capacitance n R b : buffer output resistance n t b : buffer intrinsic delay (v 1 , c 1 , q 1 ) (v 1 , c 1b , q 1b ) ECEN 687 Lecture 19

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10 Solution Propagation: Merge c merge = c l + c r q merge = min(q l , q r ) (v, c l , q l ) (v, c r , q r ) ECEN 687 Lecture 19
11 Solution Propagation: Add Driver n q 0d = q 0 – R d c 0 = Slack min n R d : driver resistance n Pick solution with max Slack min (v 0 , c 0 , q 0 ) (v 0 , c 0d , q 0d ) ECEN 687 Lecture 19

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12 Example of Solution Propagation (v 1 , 1, 20) 2 2 v 1 v 1 (v 2 , 3, 16) r = 1, c = 1 R b = 1, C b = 1, t b = 1 R d = 1 (v 2 , 1, 12) v 1 (v 3 , 5, 8) v 1 (v 3 , 3, 8) slack = 5 slack = 3 Add wire Add wire Insert buffer Add wire Add driver Add driver ECEN 687 Lecture 19
13 Example of Merging Left candid ates Right candidates Merged candidates ECEN 687 Lecture 19

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14 Solution Pruning Two candidate solutions n (v, c 1 , q 1 ) n (v, c 2 , q 2 ) Solution 1 is inferior if n c 1 > c 2 : larger load n and q 1 < q 2 : tighter timing ECEN 687 Lecture 19
15 Pruning When Insert Buffer They have the same load cap C b , only the one with max q is kept ECEN 687 Lecture 19

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• Spring '14
• Optimization, Shortest path problem, buffer solution, Buffering agent

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