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Vectorless Verification of RLC Power Grids with Transient Current ConstraintsPowerPoint Presentation

Vectorless Verification of RLC Power Grids with Transient Current Constraints

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### 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 Current Constraints

- Power Grid Verification
- Proposed Approach
- Experimental Results

Power Grid Verification Current Constraints

- 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.

Vectorless Power Grid Verification Current Constraints

- 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.

Transient Vectorless Verification Current Constraints

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.

5

Our Contribution Current Constraints

- 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

Agenda Current Constraints

- Power Grid Verification
- Proposed Approach
- Experimental Results

Integrated RLC Power Grid Current Constraints

The System Equation Current Constraints

- 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

^

Current Constraints Current Constraints

[Kouroussis et al DAC’03] and [Avci et al ICCAD’10]

- Local Constraints
- Global Constraints
- Current Conservation Constraints

Our Transient Current Constraints 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]

Our Problem Formulation Current Constraints

- For each node j
- The formulation actually computes the worst noise at node j for all time slots kt

- If the cumulative effects of voltage noises are of interests, e.g. similar to [Evmorfopoulos et al ICCAD’10], the objective function can be

Property of System Equation Current Constraints

- 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

Our Problem Decompostion Current Constraints

- 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

Agenda Current Constraints

- Power Grid Verification
- Proposed Approach
- Experimental Results

Experimental Setup Current Constraints

- 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

A Simple Case Study Current Constraints

Left: no transient constraint, max voltage drop is 118.4mV.

Right: IT = 200mA, max voltage drop at node j is 86.5mV.

Conclusion & Future Work Node

- 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.

Thanks! Node

Our RLCVN Algorithm Node

- Can be extended to verify the integral of voltage noise without any computational overhead

22

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