Topics Combinational network delay n Logic optimization n

Sources of delay n Gate delay: – drive; – load. n Wire: – lumped

Fanout n Fanout adds capacitance. sink source sink Modern VLSI Design 3 e: Chapter

Ways to drive large fanout Increase sizes of driver transistors. Must take into account

Buffers Modern VLSI Design 3 e: Chapter 4 Copyright 1998, 2002 Prentice Hall PTR

Wire capacitance Use layers with lower capacitance. n Redesign layout to reduce length of

Placement and wire capacitance g 1 g 3 g 2 g 4 dvr unbalanced

Path delay Combinational network delay is measured over paths through network. n Can trace

Path delay example network graph model Modern VLSI Design 3 e: Chapter 4 Copyright

Critical path = path which creates longest delay. n Can trace transitions which cause

Delay model Nodes represent gates. n Assign delays to edges—signal may have different delay

Critical path through delay graph Modern VLSI Design 3 e: Chapter 4 Copyright 1998,

Reducing critical path length To reduce circuit delay, must speed up the critical path—reducing

False paths Logic gates are not simple nodes—some input changes don’t cause output changes.

Logic rewrites deep logic Modern VLSI Design 3 e: Chapter 4 shallow logic Copyright

Logic transformations Can rewrite by using subexpressions. n Flattening logic increases gate fan-in. n

False path example Modern VLSI Design 3 e: Chapter 4 Copyright 1998, 2002 Prentice

Logic optimization Logic synthesis programs transform Boolean expressions into logic gate networks in a

Technology-independent optimizations Works on Boolean expression equivalence. n Estimates size based on number of

Technology-dependent optimizations Maps Boolean expressions into a particular cell library. n Mapping may take

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Ways to drive large fanout Increase sizes of driver transistors. Must take into account rules for driving large loads. n Add intermediate buffers. This may require/allow restructuring of the logic. n Modern VLSI Design 3 e: Chapter 4 Copyright 1998, 2002 Prentice Hall PTR

Path delay Combinational network delay is measured over paths through network. n Can trace a causality chain from inputs to worst-case output. n Modern VLSI Design 3 e: Chapter 4 Copyright 1998, 2002 Prentice Hall PTR

Critical path = path which creates longest delay. n Can trace transitions which cause delays that are elements of the critical delay path. n Modern VLSI Design 3 e: Chapter 4 Copyright 1998, 2002 Prentice Hall PTR

Delay model Nodes represent gates. n Assign delays to edges—signal may have different delay to different sinks. n Lump gate and wire delay into a single value. n Modern VLSI Design 3 e: Chapter 4 Copyright 1998, 2002 Prentice Hall PTR

Reducing critical path length To reduce circuit delay, must speed up the critical path—reducing delay off the path doesn’t help. n There may be more than one path of the same delay. Must speed up all equivalent paths to speed up circuit. n Must speed up cut-set through critical path. n Modern VLSI Design 3 e: Chapter 4 Copyright 1998, 2002 Prentice Hall PTR

False paths Logic gates are not simple nodes—some input changes don’t cause output changes. n A false path is a path which cannot be exercised due to Boolean gate conditions. n False paths cause pessimistic delay estimates. true path n false path Modern VLSI Design 3 e: Chapter 4 Copyright 1998, 2002 Prentice Hall PTR

Logic transformations Can rewrite by using subexpressions. n Flattening logic increases gate fan-in. n Logic rewrites may affect gate placement. n Modern VLSI Design 3 e: Chapter 4 Copyright 1998, 2002 Prentice Hall PTR

Logic optimization Logic synthesis programs transform Boolean expressions into logic gate networks in a particular library. n Optimization goals: minimize area, meet delay constraint. n Modern VLSI Design 3 e: Chapter 4 Copyright 1998, 2002 Prentice Hall PTR

Technology-independent optimizations Works on Boolean expression equivalence. n Estimates size based on number of literals. n Uses factorization, re-substitution, minimization, etc. to optimize logic. n Technology-independent phase uses simple delay models. n Modern VLSI Design 3 e: Chapter 4 Copyright 1998, 2002 Prentice Hall PTR

Technology-dependent optimizations Maps Boolean expressions into a particular cell library. n Mapping may take into account area, delay. n May perform some optimizations in addition to simple mapping. n Allows more accurate delay models. n Modern VLSI Design 3 e: Chapter 4 Copyright 1998, 2002 Prentice Hall PTR