Passive Closed-Form Transmission Line Macromodel Using Method of Characteristics

This paper presents an efficient passive time-domain macromodeling algorithm for distributed lossy transmission lines based on the generalized method of characteristics (MoC). A new theorem is described that specifies sufficient conditions to guarantee the passivity of the MoC by construction. A key feature of the proposed methodology is that the curve fitting to realize the MoC depends only on the per-unit-length (p.u.l.) parameters and not on the discretization of the macromodel. Thus, with the knowledge of the rational functions derived from the p.u.l. parameters, the MoC can be formulated in a closed-form manner for any line length while ensuring passivity.

[1]  Juliusz Poltz.  Optimizing VLSI interconnect model for SPICE simulation , 1994 .

[2]  Jr. F.H. Branin,et al.  Transient analysis of lossless transmission lines , 1967 .

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

[4]  Michel S. Nakhla,et al.  Efficient simulation of nonuniform transmission lines using integrated congruence transform , 2004, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[5]  A.C. Cangellaris,et al.  BestFit: a SPICE-compatible model for efficient, passive, broadband transmission-line analysis of dispersive interconnects , 2003, Electrical Performance of Electrical Packaging (IEEE Cat. No. 03TH8710).

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

[7]  Michel S. Nakhla,et al.  Global passivity enforcement algorithm for macromodels of interconnect subnetworks characterized by tabulated data , 2005, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[8]  Kishore Singhal,et al.  Computer Methods for Circuit Analysis and Design , 1983 .

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

[10]  Michel S. Nakhla,et al.  Passivity verification in delay-based macromodels of electrical interconnects , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[12]  Luís Miguel Silveira,et al.  A convex programming approach to positive real rational approximation , 2001, IEEE/ACM International Conference on Computer Aided Design. ICCAD 2001. IEEE/ACM Digest of Technical Papers (Cat. No.01CH37281).

[13]  Ernest S. Kuh,et al.  Passive multipoint moment matching model order reduction algorithm on multiport distributed interconnect networks , 1999 .

[14]  Anestis Dounavis,et al.  Efficient passive circuit models for distributed networks with frequency-dependent parameters , 2000 .

[15]  T. Sarkar,et al.  Closed-form formulas for frequency-dependent resistance and inductance per unit length of microstrip and strip transmission lines , 1994 .

[16]  Lawrence T. Pileggi,et al.  PRIMA: passive reduced-order interconnect macromodeling algorithm , 1997, ICCAD 1997.

[17]  Anestis Dounavis,et al.  A comparative study of two transient analysis algorithms for lossy transmission lines with frequency-dependent data , 2001 .

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

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

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

[21]  C. S. Chang,et al.  Coupled lossy transmission line characterization and simulation , 1981 .

[22]  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.

[23]  J. L. Prince,et al.  A new discrete transmission line model for passive model order reduction and macromodeling of high-speed interconnections , 1999 .

[24]  Louis Weinberg,et al.  Network Analysis and Synthesis , 1962 .

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

[26]  Anestis Dounavis,et al.  Efficient passive transmission line macromodeling algorithm using method of characteristics , 2006, 2006 IEEE International Symposium on Circuits and Systems.

[27]  Ernest S. Kuh,et al.  Transient simulation of lossy interconnects based on the recursive convolution formulation , 1992 .

[28]  E. Guillemin.  Synthesis of passive networks : theory and methods appropriate to the realization and approximation problems , 1957 .

[29]  T. Sarkar,et al.  Evaluation of quasi-static matrix parameters for multiconductor transmission lines using Galerkin's method , 1994 .

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

[31]  Robert H. Dennard,et al.  Modeling and characterization of long on-chip interconnections for high-performance microprocessors , 1995, IBM Journal of Research and Development.