Transcript Presentation kit

Vectorless Verification of RLC
Power Grids with Transient
Current Constraints
Xuanxing Xiong and Jia Wang
Electrical and Computer Engineering
Illinois Institute of Technology
Chicago, Illinois, United States
November, 2011
Agenda
 Power Grid Verification
 Proposed Approach
 Experimental Results
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Power Grid Verification
 Verify that the power supply noises are within certain
acceptable range

Noises depend on the patterns of currents drawn
 General idea for power grid verification
First, specify currents
 Second, compute noises

 Simulation-based verification
DC & Transient analysis
 Need to simulate a large number of current vectors to cover
usual use scenarios
 No guarantee the worst noise (but not overpessimistic) can be
found.

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Vectorless Power Grid Verification
 Apply optimization to find a current vector that leads
to the worst power supply noise
[Kouroussis et al DAC’03] [Qian et al ISPD’04]
 Objective: maximizing power supply noise
 Constraints: feasible current set  all possible current vectors
 No need to explicitly enumerate all possible current vectors
 Trade-off: accuracy of feasible current set and solution
efficiency

Linear current constraints: linear programming
 Steady-state vectorless verification
For worst-case DC scenarios and provide bounds for RC
powergrid.
 Early works are limited to small problem sizes. But recent
advances [Abdul Ghani et al DAC’09] [Xiong et al DAC’10,
ICCAD’10] have improved solution efficiency drastically.

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Transient Vectorless Verification
 Transient behaviors are more realistic

Steady-state verification could be overpessimistic.
 Power grid modeling


Inductances [Abdul Ghani et al ICCAD’06]
Capacitive couplings between VDD and GND networks
[Avci et al ICCAD’10]
 Current modeling




Max delta constraints [Ferzli et al TCAD’10]
Current slope constraints [Du et al ISQED’10]
Current conservation constraints [Avci et al ICCAD’10]
Power constraints [Cheng et al ISPD’11]
 However, there is no constraint to restrict the
transient behavior of individual current sources.
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Our Contribution
 A framework for transient vectorless verification of
RLC power grids

With both VDD & GND networks
 Propose transient constraints for current sources

To capture the fact that a gate/block will only draw current
when it is switching
 Prove the transient vectorless verification problem
can be decomposed into a transient power grid
anlysis problem and an optimization problem

Be able to leverage research works on fast power grid
simulation
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Agenda
 Power Grid Verification
 Proposed Approach
 Experimental Results
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Integrated RLC Power Grid
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The System Equation
 Time domain

G: conductance
M/C: represent self-inductance/capactiance links
 v(t): nodal voltage noises
^
 I(t): current excitations

 Discretization with time step t
where
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Current Constraints
[Kouroussis et al DAC’03] and [Avci et al ICCAD’10]
 Local Constraints
 Global Constraints
 Current Conservation Constraints
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Our Transient Current Constraints
 Nts: number of time steps
 IT: nx1 upper bound vector
 Transient constraints may be extracted from the
circuit by switching activity analysis, e.g.
[Morgado et al ICSD’09] and [Morgado et al TODAES’09]
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Our Problem Formulation
 For each node j

The formulation actually computes the worst noise at
node j for all time slots kt
 If the cumulative effects of voltage noises are of
interests, e.g. similar to [Evmorfopoulos et al
ICCAD’10], the objective function can be
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Property of System Equation
 There exists a unique series of nxn matrices S1, S2, ...
Sk, Sk+1, ..., such that
 jth column of Sk can be computed as
 Sk is symmetric. So
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Our Problem Decompostion
 For each node j:
 Sub-problem I: transient analysis with current
excitation ej to compute cj,k
 Sub-problem II: linear programming (LP) to compute
worst-case voltage noises
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Agenda
 Power Grid Verification
 Proposed Approach
 Experimental Results
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Experimental Setup
 Implement the RLCVN in C++
Use PCG with a random-walk based preconditioner for
transient analysis
 Adopt MOSEK to solve the LP problems

 Randomly generate 6 RLC power grids with 4 metal
layers, 1.2V VDD, and various constraints
 Time step = 10ps, number of time steps Nts = 100
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A Simple Case Study
Left: no transient constraint, max voltage drop is 118.4mV.
Right: IT = 200mA, max voltage drop at node j is 86.5mV.
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Overestimation without Transient
Constraints for a Random Node
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Average Runtime per Node
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Conclusion & Future Work
 The proposed transient constraints make the voltage
noise predicitons more realistic.
 The proposed decomposition results in an effective
method for transient vectorless verification.
 To handle even larger power grid verification
problems, it is necessary to research more efficient
algorithms to solve the LP problems for worst-case
voltage noises.
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Thanks!
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Our RLCVN Algorithm
 Can be extended to verify the integral of voltage
noise without any computational overhead
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