Waveform Relaxation Techniques for Simulation of Coupled Interconnects With Frequency-Dependent Parameters

The large number of coupled lines in an interconnect structure is a serious limiting factor in simulating high-speed circuits. Waveform relaxation based on transverse partitioning has been previously presented to address this problem for interconnects with constant per-unit-length parameters. This paper extends the waveform relaxation technique to handle the more difficult and important case of frequency-dependent parameters. The computational cost of the proposed algorithm grows linearly with the number of coupled lines

[1]  Rui Wang,et al.  Transient analysis of dispersive VLSI interconnects terminated in nonlinear loads , 1992, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[2]  Albert E. Ruehli,et al.  Physically consistent transmission line models for high-speed interconnects in lossy dielectrics , 2001 .

[3]  Fung-Yuel Chang.  Waveform relaxation analysis of RLCG transmission lines , 1990 .

[4]  Albert E. Ruehli,et al.  Circuit Analysis Computing by Waveform Relaxation , 1999 .

[5]  Fung-Yuel Chang.  The generalized method of characteristics for waveform relaxation analysis of lossy coupled transmission lines , 1989 .

[6]  Alberto L. Sangiovanni-Vincentelli,et al.  The Waveform Relaxation Method for Time-Domain Analysis of Large Scale Integrated Circuits , 1982, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[7]  R. Achar,et al.  A fast algorithm and practical considerations for passive macromodeling of measured/simulated data , 2004, IEEE Transactions on Advanced Packaging.

[8]  T. Sarkar,et al.  Analysis of Multiconductor Transmission Lines , 1988, 31st ARFTG Conference Digest.

[9]  Philip Rabinowitz,et al.  Methods of Numerical Integration , 1985 .

[10]  J. White,et al.  Relax2: a Modified Waveform Relaxation Approach , .

[11]  R. Achar,et al.  Efficient sensitivity analysis of lossy multiconductor transmission lines with nonlinear terminations , 2001, 2001 IEEE MTT-S International Microwave Sympsoium Digest (Cat. No.01CH37157).

[12]  Qing-Xin Chu,et al.  Transient analysis of microwave active circuits based on time-domain characteristic models , 1998 .

[13]  U. Miekkala,et al.  Convergence of waveform relaxation method , 1988, 1988., IEEE International Symposium on Circuits and Systems.

[14]  J. Szabados,et al.  Interpolation of Functions , 1990 .

[15]  Jose E. Schutt-Aine,et al.  Optimal transient simulation of transmission lines , 1996 .

[16]  M. Nakhla,et al.  Delay extraction and passive macromodeling of lossy coupled transmission lines , 2003, Electrical Performance of Electrical Packaging (IEEE Cat. No. 03TH8710).

[17]  Jiri Vlach,et al.  Computerized approximation and synthesis of linear networks , 1969 .

[18]  Alberto Sangiovanni-Vincentelli,et al.  Partitioning Algorithms And Parallel Implementations Of Waveform Relaxation Algorithms For Circuit S , 1985 .

[19]  Michel Nakhla,et al.  Simulation of coupled interconnects using waveform relaxation and transverse partitioning , 2006 .

[20]  Ramachandra Achar,et al.  A general class of passive macromodels for lossy multiconductor transmission lines , 2001 .

[21]  A.C. Cangellaris,et al.  Three test problems for the comparison of lossy transmission line algorithms , 2002, Electrical Performance of Electronic Packaging,.

[22]  A. Semlyen,et al.  Rational approximation of frequency domain responses by vector fitting , 1999 .

[23]  R. Achar,et al.  DEPACT: delay extraction-based passive compact transmission-line macromodeling algorithm , 2005, IEEE Transactions on Advanced Packaging.

[24]  Stefano Grivet-Talocia,et al.  Passivity enforcement via perturbation of Hamiltonian matrices , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[25]  S. Grivet-Talocia,et al.  Transient analysis of lossy transmission lines: an efficient approach based on the method of Characteristics , 2004, IEEE Transactions on Advanced Packaging.

[26]  Jacob K. White,et al.  Relaxation Techniques for the Simulation of VLSI Circuits , 1986 .

[27]  Ramachandra Achar,et al.  Simulation of high-speed interconnects , 2001, Proc. IEEE.