An Instrumental Variable Vector-Fitting Approach for Noisy Frequency Responses

This paper presents an efficient methodology to improve the convergence properties of vector fitting (VF) when the frequency data is contaminated by noise. The proposed algorithm uses an instrumental variable approach, which minimizes the biasing effect of the least squares solution caused by the noise of the data samples. These instruments are generated using the rational approximation of the previous iteration and does not increase the computational complexity of the VF algorithm. Numerical examples are provided to illustrate the validity of the proposed method.

[1]  A. Semlyen,et al.  A robust approach for system identification in the frequency domain , 2004, IEEE Transactions on Power Delivery.

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

[3]  B. Gustavsen,et al.  Computer Code for Rational Approximation of Frequency Dependent Admittance Matrices , 2002, IEEE Power Engineering Review.

[4]  Biao Huang,et al.  System Identification , 2000, Control Theory for Physicists.

[5]  A Multivariate Orthonormal Vector Fitting based estimation technique , 2009 .

[6]  Albert E. Ruehli,et al.  Systematic development of transmission line models for interconnects with frequency-dependent losses , 2000, IEEE 9th Topical Meeting on Electrical Performance of Electronic Packaging (Cat. No.00TH8524).

[7]  Alex Simpkins,et al.  System Identification: Theory for the User, 2nd Edition (Ljung, L.; 1999) [On the Shelf] , 2012, IEEE Robotics & Automation Magazine.

[8]  Er-Ping Li,et al.  A coupled efficient and systematic full-wave time-domain macromodeling and circuit Simulation method for signal integrity analysis of high-speed interconnects , 2004, IEEE Transactions on Advanced Packaging.

[9]  En-Xiao Liu,et al.  Analysis of signal propagation on high-speed planar interconnect systems based on full-wave and macromodeling techniques , 2003 .

[10]  T. Dhaene,et al.  Variance Weighted Vector Fitting for Noisy Frequency Responses , 2010, IEEE Microwave and Wireless Components Letters.

[11]  A. Semlyen,et al.  Combined phase and modal domain calculation of transmission line transients based on vector fitting , 1998 .

[12]  David D. Wentzloff,et al.  IEEE Transactions on Microwave Theory and Techniques and Antennas and Propagation Announce a Joint Special Issue on Ultra-Wideband (UWB) Technology , 2010 .

[13]  M. Nakhla,et al.  A fast algorithm and practical considerations for passive macromodeling of measured/simulated data , 2002, Electrical Performance of Electronic Packaging,.

[14]  Adam Semlyen,et al.  Vector fitting by pole relocation for the state equation approximation of nonrational transfer matrices , 2000 .

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

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

[17]  Hong Wang,et al.  Recursive estimation and time-series analysis , 1986, IEEE Trans. Acoust. Speech Signal Process..

[18]  T. Söderström,et al.  Instrumental variable methods for system identification , 1983 .

[19]  B. Nouri,et al.  $z$ -Domain Orthonormal Basis Functions for Physical System Identifications , 2010, IEEE Transactions on Advanced Packaging.

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

[21]  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.

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

[23]  Rik Pintelon,et al.  System Identification: A Frequency Domain Approach , 2012 .

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

[25]  T. Dhaene,et al.  Advancements in Iterative Methods for Rational Approximation in the Frequency Domain , 2007, IEEE Transactions on Power Delivery.

[26]  Jose E. Schutt-Aine,et al.  Efficient transient simulation of high-speed interconnects characterized by sampled data , 1996 .

[27]  B. Gustavsen.  Relaxed Vector Fitting Algorithm for Rational Approximation of Frequency Domain Responses , 2006, 2006 IEEE Workship on Signal Propagation on Interconnects.

[28]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

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