Xuanxing Xiong and Jia Wang Electrical and Computer Engineering Illinois Institute of Technology...
-
Upload
jordan-hawkins -
Category
Documents
-
view
220 -
download
0
Transcript of Xuanxing Xiong and Jia Wang Electrical and Computer Engineering Illinois Institute of Technology...
Xuanxing Xiong and Jia Wang
Electrical and Computer EngineeringIllinois Institute of TechnologyChicago, Illinois, United States
November, 2011
Vectorless Verification of RLC Power Grids with Transient
Current Constraints
Vectorless Verification of RLC Power Grids with Transient
Current Constraints
AgendaAgenda
Power Grid Verification
Proposed Approach
Experimental Results
2
Power Grid VerificationPower 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.
3
Vectorless Power Grid VerificationVectorless 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.
4
Transient Vectorless VerificationTransient 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.
5
Our ContributionOur 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
6
AgendaAgenda
Power Grid Verification
Proposed Approach
Experimental Results
7
Integrated RLC Power GridIntegrated RLC Power Grid
8
The System EquationThe 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
9
^
Current ConstraintsCurrent Constraints
[Kouroussis et al DAC’03] and [Avci et al ICCAD’10]
Local Constraints
Global Constraints
Current Conservation Constraints
10
Our Transient Current ConstraintsOur 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]
11
Our Problem FormulationOur Problem Formulation
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
12
Property of System EquationProperty of System Equation
13
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 DecompostionOur Problem Decompostion
14
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
AgendaAgenda
Power Grid Verification
Proposed Approach
Experimental Results
15
Experimental SetupExperimental 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
16
A Simple Case StudyA Simple Case Study
17
Left: no transient constraint, max voltage drop is 118.4mV.Right: IT = 200mA, max voltage drop at node j is 86.5mV.
Overestimation without Transient Constraints for a Random NodeOverestimation without Transient Constraints for a Random Node
18
Average Runtime per NodeAverage Runtime per Node
19
Conclusion & Future WorkConclusion & 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.
20
Thanks!Thanks!
21
Can be extended to verify the integral of voltage noise without any computational overhead
Our RLCVN AlgorithmOur RLCVN Algorithm
22