Efficient Linear Macromodeling via Discrete-Time Time-Domain Vector Fitting

We present a discrete-time time-domain vector fitting algorithm, called TD-VFz, for rational function macromodeling of port-to-port responses with discrete time-sampled data. The core routine involves a two-step pole refinement process based on a linear least-squares solve and an eigenvalue problem. Applications in the macromodeling of practical circuits demonstrate that TD-VFz exhibits fast computation, excellent accuracy, and robustness against noisy data. We also utilize an quasi-error bound unique to the discrete-time setting to facilitate the determination of approximant model order.

[1]  B. Gustavsen,et al.  Improving the pole relocating properties of vector fitting , 2006, 2006 IEEE Power Engineering Society General Meeting.

[2]  Madhavan Swaminathan,et al.  Delay extraction from frequency domain data for causal macro-modeling of passive networks , 2005, 2005 IEEE International Symposium on Circuits and Systems.

[3]  Zhizhang Chen,et al.  Extraction of causal time-domain network parameters from their band-limited frequency-domain counterparts using rational functions , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[4]  C. Sanathanan,et al.  Transfer function synthesis as a ratio of two complex polynomials , 1963 .

[5]  E. Seebacher,et al.  Compact modeling and fast simulation of on-chip interconnect lines , 2006, IEEE Transactions on Magnetics.

[6]  S. Grivet-Talocia,et al.  Improving the convergence of vector fitting for equivalent circuit extraction from noisy frequency responses , 2006, IEEE Transactions on Electromagnetic Compatibility.

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

[8]  S. Grivet-Talocia,et al.  Package macromodeling via time-domain vector fitting , 2003, IEEE Microwave and Wireless Components Letters.

[9]  M. Mboup,et al.  Undermodeled adaptive filtering: an a priori error bound for the Steiglitz-McBride method , 1996 .

[10]  T. Dhaene,et al.  Orthonormal Vector Fitting: A Robust Macromodeling Tool for Rational Approximation of Frequency Domain Responses , 2007, IEEE Transactions on Advanced Packaging.

[11]  Larry Pileggi,et al.  IC Interconnect Analysis , 2002 .

[12]  L. Mcbride,et al.  A technique for the identification of linear systems , 1965 .

[13]  Tzong-Lin Wu,et al.  A novel systematic approach for equivalent model extraction of embedded high-speed interconnects in time domain , 2003 .

[14]  Ngai Wong,et al.  IIR Approximation of FIR Filters Via Discrete-Time Vector Fitting , 2008, IEEE Transactions on Signal Processing.

[15]  J.H. Sinsky,et al.  Modified Rational Function Modeling Technique for High Speed Circuits , 2006, 2006 IEEE MTT-S International Microwave Symposium Digest.