Denis Kouroussis, Imad Ferzli, Farid Najm

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• Denis Kouroussis, Imad Ferzli, Farid Najm

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Verification Robust Grid Design

• Timing violations, small noise margins,
  electromigration compounded by scaling trends
• How do we design robust grids without overusing
  metal resources?
• Over-design or under-design then refine?
• Efficient verification key to robust power grid
  design

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What The Fed Thinks

• Like a breakdown in an electric power grid,
  small mishaps create large problems
• Alan Greenspan

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Grid Verification Objective List

• Vectorless
• Does not rely on test vectors!
• Opposite simulation-based
• Think of STA!
• Applicable early in the design cycle
• Useful when change can be easily made
• Incremental
• Targets a specific grid block think of IP blocks
• Corrections and changes often incremental

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Constraint-Based Verification

• If no information available about circuit, no
  power grid verification possible!
• Put to use engineering judgment and design
  expertise to verify grid
• Spec-based design framework
• One way is to use constraints on circuit currents

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Constraint-Based Verification

• Constraints capture current uncertainty arising
  from
• Circuit behavior, given the large number of
  possible input vectors (vectorless verification)
• Lack of knowledge of circuit details early in the
  design flow
• Examples are upper bounds on currents
• What is the maximum voltage drop under current
  constraints?

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Local Constraints

• Expressed as
• Alone they are equivalent to worst-case current
  traces

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Global Constraints

• One way to capture joint behavior is through a
  bound on current drawn by a group of current
  sources simultaneously
• Expressed as
• For n power grid nodes, k global constraints, U
  is a k x n matrix of 0s and 1s

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Example
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How Do We Get Constraints?

• Design expertise!

Fallback
New design
Existing design
Power density, area
Engineering judgment, scaling
Simulation
Block small
Design expertise, scaling
Block large
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Incremental Verification
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Incremental Verification

• Partition grid to remove nodes outside the block
  under verification
• Macromodeling is relevant
• Not directly applicable to grid verification
• Leverage macromodeling concepts to enable
  constraint-based grid verification

M. Zhao, R.V. Panda, S.S. Sapatnekar, and D.
Blaauw, Hierarchical analysis of power
distribution networks, IEEE Trans.
Computer-Aided Design, vol. 21, no 2,
pp. 159-168, Feb. 2002.
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Grid Partitioning Before After
Before
After
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Mapping Local Constraints

• Local constraints on ports increase
• Mapping function of external constraints, grid
  connectivity
• Local constraints on internal nodes unchanged

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Mapping Local Constraints
Before
After
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Mapping Global Constraints

• Same idea as local constraints
  map global constraints involving external
  currents to port nodes
• Mapping function of external global constraints
  and conductance matrix
• Caveat partitioning cannot be arbitrary!

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Partitioning for Grid Verification
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Partitioning for Grid Verification

• Culprit is the external part of the global
  constraint matrix
• Need for mapping to be possible
• and are related

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Partitioning for Grid Verification

• External global constraints, C4s add their own
  port nodes to the partition

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Illustration Grid Reduction
Before
After
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Illustration Global Constraints
Before
After
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Mapping Is Conservative
Before
After
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Pros Cons of Partitioning

• Incremental block verification within large
  grids possible, efficient

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Grid Locality Considerations

• Nodes are mostly influenced by currents drawn in
  a neighborhood around them
• C4s, decaps average the effect of faraway
  currents on a given grid node
• Refine constraint-based verification by allowing
  fixed values, not constraints, for all (or
  selected) external current sources

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Grid Locality Considerations
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What We Gain with Locality

• Drastic macromodeling
  keep only desired block under
  verification
• Lossless mapping
  no over-estimation compared to
  flat case
• Which currents to fix and at what values are
  knobs in designers hands
• Consideration to distance, switching activity,
  strength of current sink, grid connectivity

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Grid Verification with Locality
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Example
Partitioning with locality
Flat solution with locality
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Results With Locality
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Conclusion

• Verified power grid in a constraint-based design
  framework
• Leveraged grid locality to simplify the problem
• Enabled incremental grid verification on
  large-size grids