Dual Algorithms for Vectorless Power Grid Verification Under Linear Current Constraints

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

2013

Vectorless power grid verification is a powerful method that evaluates worst-case voltage noises without detailed current waveforms using optimization techniques. It is extremely challenging when considering RLC power grids because inductors are difficult to tackle and multiple time steps should be evaluated after the discretization of the system equation. In this paper, we study integrated RLC power grids with both VDD and GND networks, and introduce transient constraints to restrict the waveform of each current source for sign-off verification. We rigorously prove that the vectorless verification can be decomposed into two subproblems-the well-studied power grid transient analysis problem and a linear programming (LP) problem that optimizes an affine function of currents under current constraints-and propose to verify the power grid by transient simulation and noise optimization. A variable reduction algorithm is further proposed to generate reduced-size LP problems with a user-specified error tolerance, so that the conservative bounds of voltage noises can be computed efficiently. Experimental results show that the proposed algorithm achieves significant speedup (e.g., up to more than 100× with 5 mV error) over the standard LP solver in solving the LP problems, and the proposed transient constraints make the noise estimations more realistic.

Section: Problem Decompositionmentioning

confidence: 99%

mentioning

confidence: 99%

Verifying RLC Power Grids With Transient Current Constraints

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

2013

“…The initial study [13] considered the DC analysis model, and it was extended to verify RC power grids in [8]. Since solving the linear programs is very expensive, [3] proposed to generate a reduced-size linear program for each node by using an approximate inverse technique; [17] and [19] designed convex dual algorithms to solve the linear programs efficiently; [1] utilized the dominance relations among nodal voltage drops to reduce the number of linear programs to be solved; [12] and [5] used macromodeling technique to simplify the linear programs for efficient incremental verification. Besides, [6] proposed to verify VDD network and ground network together with additional current conservation constraints in order to consider the mutual effects in between.…”

Section: Introductionmentioning

confidence: 99%

Constraint abstraction for vectorless power grid verification

Proceedings of the 50th Annual Design Automation Conference

2013

Self Cite

Vectorless power grid verification is a formal approach to analyze power supply noises across the chip without detailed current waveforms. It is typically formulated and solved as linear programs, which demand intensive computational power, especially for large-scale power grids. In this paper, we propose a constraint abstraction technique to reduce the computation cost of vectorless verification. The boundary condition of a subgrid is modeled by boundary constraints, which enable efficient calculation of conservative bounds of power supply noises in a divide-and-conquer manner. Experimental results show that the proposed approach achieves significant speedup over prior art while maintaining good solution quality.

“…To enable early power grid verification, vectorless verification approaches have been proposed [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17]. These approaches use linear current constraints to restrict the feasible set of all possible current waveforms, then solve linear programming (LP) problems to evaluate the worst-case voltage noise.…”

Section: Introductionmentioning

confidence: 99%

“…The initial vectorless approach [7] considers the DC analysis model, and it is extended to handle RC and RLC power grids in [8] and [9], respectively. Reference [10] uses an approximate inverse technique to generate a reduced-size LP problem for each node, [11] designs a hierarchical matrix inversion algorithm to compute the inverse of the power grid matrix, [12] and [13] propose convex dual algorithms to solve the LP problem fast. Besides, wavelet analysis is employed in [14] to characterize current excitations in order to identify the worst-case voltage fluctuations.…”

Section: Introductionmentioning

confidence: 99%

Vectorless verification of RLC power grids with transient current constraints

2011 IEEE/ACM International Conference on Computer-Aided Design (ICCAD)

2011

Self Cite

Abstract-Vectorless power grid verification is a powerful method that evaluates worst-case voltage noises without detailed current waveforms using optimization techniques. It is extremely challenging when considering RLC power grids since inductors are difficult to tackle and multiple time steps should be evaluated after the discretization of the system equation. In this paper, we study integrated RLC power grids with both VDD and GND networks and rigorously prove that their vectorless verification can be decomposed into two sub-problems -the well-studied transient power grid analysis problem and an optimization problem that maximizes an affine function of currents under current constraints. We further introduce transient constraints to restrict the waveform of each current source for realistic scenarios and design the RLCVN algorithm to solve the vectorless verification problem of RLC power grids. Results confirm that our algorithm is an effective approach for practical RLC power grid verification, and the proposed transient constraints make the noise estimations more realistic.