Power grid transient simulation in linear time based on transmission-line-modeling alternating-direction-implicit method

The soaring clocking frequency and integration density demand robust and stable power delivery to support tens of millions of transistors switching. To ensure the design quality of power delivery, extensive transient power grid simulations need to be performed during design process. However, the traditional circuit simulation engines are not scaled as well as the complexity of power delivery, as a result, it often takes a long runtime and huge memory requirement to simulate a medium size power grid circuit. We develop and present a new efficient transient simulation algorithm for power distribution. The proposed algorithm, TLM-ADI (transmission-line-modeling alternatingdirection-implicit), first models the power delivery structure as transmission line mesh structure, then solves the transient MNA matrices by the alternating-direction-implicit method. The proposed algorithm, with linear runtime and memory requirement, is also unconditionally stable which ensures that the time-step is not limited by any stability requirement. Extensive experimental results show that the proposed algorithm is not only orders of magnitude faster than SPICE but also extremely accurate.

[1]  Rajendran Panda,et al.  Hierarchical analysis of power distribution networks , 2000, DAC.

[2]  Rajendran Panda,et al.  Design and analysis of power distribution networks in PowerPC microprocessors , 1998, DAC.

[3]  Charlie Chung-Ping Chen,et al.  Generalized FDTD-ADI: an unconditionally stable full-wave Maxwell's equations solver for VLSI interconnect modeling , 2000, IEEE/ACM International Conference on Computer Aided Design. ICCAD - 2000. IEEE/ACM Digest of Technical Papers (Cat. No.00CH37140).

[4]  C. Christopoulos,et al.  The Transmission-line Modeling Method: TLM , 1995, IEEE Antennas and Propagation Magazine.

[5]  Charlie Chung-Ping Chen,et al.  Efficient large-scale power grid analysis based on preconditioned Krylov-subspace iterative methods , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).

[6]  Fenghua Zhen,et al.  Toward the development of a three-dimensional unconditionally stable finite-difference time-domain method , 2000 .

[7]  Madhavan Swaminathan,et al.  Modeling of power distribution networks for mixed signal applications , 2001, 2001 IEEE EMC International Symposium. Symposium Record. International Symposium on Electromagnetic Compatibility (Cat. No.01CH37161).

[8]  Wojciech Gwarek,et al.  Analysis of arbitrarily shaped two-dimensional microwave circuits by finite-difference time-domain method , 1988 .

[9]  H. H. Rachford,et al.  The Numerical Solution of Parabolic and Elliptic Differential Equations , 1955 .

[10]  Sani R. Nassif,et al.  Fast power grid simulation , 2000, Proceedings 37th Design Automation Conference.

[11]  T. Namiki,et al.  A new FDTD algorithm based on alternating-direction implicit method , 1999 .

[12]  J. Strikwerda.  Finite Difference Schemes and Partial Differential Equations , 1989 .

[13]  Allen Taflove,et al.  Computational Electrodynamics the Finite-Difference Time-Domain Method , 1995 .

[14]  Miodrag Potkonjak,et al.  On-line fault detection for bus-based field programmable gate arrays , 1998, IEEE Trans. Very Large Scale Integr. Syst..

[15]  Kwang-Ting Cheng,et al.  Analysis of performance impact caused by power supply noise in deep submicron devices , 1999, DAC '99.

[16]  Larry L. Biro,et al.  Power considerations in the design of the Alpha 21264 microprocessor , 1998, Proceedings 1998 Design and Automation Conference. 35th DAC. (Cat. No.98CH36175).

[17]  David D. Ling,et al.  Power Supply Noise Analysis Methodology For Deep-submicron Vlsi Chip Design , 1997, Proceedings of the 34th Design Automation Conference.

[18]  Christos Christopoulos,et al.  transmission-line modeling method , 1995 .

[19]  Rajendran Panda,et al.  Design and analysis of power distribution networks in PowerPCTM microprocessors , 1998, DAC 1998.