ABSTRACT
The integration of more components into modern Systems-on-Chip (SoCs) has led to very large RLC parasitic networks consisting of million of nodes, which have to be simulated in many times or frequencies to verify the proper operation of the chip. Model Order Reduction techniques have been employed routinely to substitute the large scale parasitic model by a model of lower order with similar response at the input/output ports. However, all established MOR techniques result in dense system matrices that render their simulation impractical. To this end, in this paper we propose a methodology for the sparsification of the dense circuit matrices resulting from Model Order Reduction of general RLC circuits, which employs a sequence of algorithms based on the computation of the nearest diagonally dominant matrix and the sparsification of the corresponding graph. Experimental results indicate that a high sparsity ratio of the reduced system matrices can be achieved with very small loss of accuracy.
- Z. Ye, D. Vasilyev, Z. Zhu and J. R. Phillips, Sparse Implicit Projection (SIP) for reduction of general many-terminal networks, IEEE/ACM International Conference on Computer-Aided Design, 2008. Google Scholar
Digital Library
- P. Miettinen, M. Honkala, J. Roos, M. Valtonen, PartMOR: Partitioning-Based Realizable Model-Order Reduction Method for RLC Circuits, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 30, pp. 374--387, 2011. Google Scholar
Digital Library
- H. Yu, C. Chu, Y. Shi, D. Smart L. He and S. X.-D. Tan Fast Analysis of Large Scale Inductive Interconnect by Block Structure Preserved Macromodeling, IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 18, pp. 1399--1411, 2009. Google Scholar
Digital Library
- C. Antoniadis, N. Evmorfopoulos and G. Stamoulis, Efficient Sparsification of Dense Circuit Matrices in Model Order Reduction, Asia and South Pacific Design Automation Conference, 2019. Google Scholar
Digital Library
- A. E. Ruehli, Circuit Analysis, Simulation and Design, Part 1, New York: North-Holland, 1986. Google Scholar
Digital Library
- R. Horn and C. Johnson, Matrix Analysis, Cambridge University Press, 1985. Google Scholar
Digital Library
- A. Devgan, H. Ji, and W. Dai, How to Efficiently Capture On-Chip Inductance Effects: Introducing a New Circuit Element K, IEEE/ACM International Conference on Computer-Aided Design, 2000. Google Scholar
Digital Library
- R. Merris, Laplacian matrices of a graph: A survey, Linear Algebra and its Applications, vol. 197, pp. 143--176, 1994.Google Scholar
Cross Ref
- Freud R. W., SPRIM: structure-preserving reduced-order interconnect macromodeling., IEEE/ACM International Conference on Computer-Aided Design, 2004. Google Scholar
Digital Library
- Y. Su, J. Wang, X. Zeng, Z. Bai, C. Chiang, D. Zhou SAPOR: second-order Arnoldi method for passive order reduction of RCS circuits, IEEE/ACM International Conference on Computer Aided Design, 2004. Google Scholar
Digital Library
- M. Mendoza, M. Raydan and P. Tarazaga, Computing the nearest diagonally dominant matrix, Numerical Linear Algebra with Applications, vol. 5, pp. 461--474, 1998.Google Scholar
Cross Ref
- J.P. Boyle and R.L. Dykstra, A Method for Finding Projections onto the Intersection of Convex Sets in Hilbert Spaces, Springer, 1986.Google Scholar
Cross Ref
- M. Monsalve, J. Moreno, R. Escalante and M. Raydan, Selective alternating projections to find the nearest SDD+ matrix, Applied Mathematics and Computation, vol. 145, pp. 205--220, 2003. Google Scholar
Digital Library
- K.D. Gremban, Combinatorial Preconditioners for Sparse, Symmetric, Diagonally Dominant Linear Systems, Ph.D. thesis, Carnegie-Mellon University, Department of Computer Science, 1996.Google Scholar
- D. Spielman and N. Srivastava, Graph Sparsification by Effective Resistances, SIAM Journal on Computing, vol. 40, pp. 1913--1926, 2011. Google Scholar
Digital Library
- D. Achlioptas, Database-friendly Random Projections, ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, 2001. Google Scholar
Digital Library
- D. Spielman and S.H. Teng, Nearly-linear Time Algorithms for Graph Partitioning, Graph Sparsification, and Solving Linear Systems, ACM Symposium on Theory of Computing, 2004. Google Scholar
Digital Library
- I. Koutis, G.L. Miller and R. Peng, A nearly-m logn solver for SDD linear systems, IEEE Symposium on Foundations of Computer Science, 2011. Google Scholar
Digital Library
- F. Yang, X. Zeng, Y. Su, D. Zhou, RLCSYN: RLC Equivalent Circuit Synthesis for Structure-Preserved Reduced-order Model of Interconnect, IEEE International Symposium on Circuits and Systems, 2007.Google Scholar
- M. Kamon, M. J. Tsuk and J. K. White, FASTHENRY: a multipole-accelerated 3-D inductance extraction program, IEEE Transactions on Microwave Theory and Techniques, vol. 42, pp. 1750--1758, Sept. 1994.Google Scholar
Cross Ref
Recommendations
Efficient sparsification of dense circuit matrices in model order reduction
ASPDAC '19: Proceedings of the 24th Asia and South Pacific Design Automation ConferenceThe integration of more components into ICs due to the ever increasing technology scaling has led to very large parasitic networks consisting of million of nodes, which have to be simulated in many times or frequencies to verify the proper operation of ...
Device circuit co-design to reduce gate leakage current in VLSI logic circuits in nano regime
In this paper, nanoscale metal-oxide-semiconductor field-effect transistor MOSFET device circuit co-design is presented with an aim to reduce the gate leakage curren t in VLSI logic circuits. Firstly, gate leakage current is modeled through high-k ...
ONOFIC Pull-Up Approach in Domino Logic Circuits Using FinFET for Subthreshold Leakage Reduction
In this paper, ON/OFf logIC (ONOFIC) approach is applied in pull-up network of domino Fin Field-Effect Transistor (FinFET) gates. With this approach, 2-, 4-, 8- and 16-input OR gates are simulated with 32-nm FinFET technology node and compared with ...





Comments