# References

Vector Fitting, Passivity, Compacting

- B. Gustavsen and A. Semlyen, "Rational approximation of frequency domain responses by vector fitting", IEEE Trans. Power Delivery, vol. 14, no. 3, pp. 1052-1061, July 1999.
**PDF** - A. Semlyen and B. Gustavsen, "Vector fitting by pole relocation for the state equation approximation of nonrational transfer matrices", Circuits Systems Signal Process, vol. 19, no. 6, pp. 549-566, 2000.
**PDF** - B. Gustavsen and A. Semlyen, "Enforcing passivity for admittance matrices approximated by rational functions", IEEE Trans. Power Systems, vol. 16, no. 1, pp. 97-104, Feb. 2001.
**PDF** - B. Gustavsen, "Computer code for rational approximation of frequency dependent admittance matrices", IEEE Trans. Power Delivery, vol. 17, no. 4, pp. 1093-1098, Oct. 2002.
**PDF** - B. Gustavsen and A. Semlyen, "A robust approach for system identification in the frequency domain", IEEE Trans. Power Delivery, vol. 19, no. 3, pp. 1167-1173, July 2004.
**PDF** - S. Grivet-Talocia, “Package Macromodeling via Time-Domain Vector Fitting”, IEEE Microwave and Wireless Components Letters, vol. 13, no. 11, pp. 472-474, Nov. 2003.
- S. grivet-Talocia, “Enforcing Passivity of macromodels via Spectral Perturbation of Hamiltonian matrices”, 7th IEEE Workshop on Signal Propagation on Interconnects (SPI), Siena, Italy, pp. 33-36. May 11-14, 2003.
- D. Saraswat, R. Achar and M. Nakhla, “A Fast Algorithm and Practical Considerations for Passive Macromodeling of Measured/Simulated Data”, IEEE Trans. Advanced Packaging, vol. 27, no. 1, pp. 57-70, Feb. 2004.
- D. Deschrijver and T. Dhaene, “Rational modeling of spectral data using orthonormal vector fitting”, 9th IEEE Workshop on Signal Propagation on Interconnects (SPI), pp. 111-114, 2005.
- B. Gustavsen, “Computer code for passivity enforcement of rational macromodels”, 9th IEEE Workshop on Signal Propagation on Interconnects (SPI), pp. 115-118, 2005.
**PDF** - B. Gustavsen, ”Improving the pole relocating properties of vector fitting”, IEEE Trans. Power Delivery, vol. 21, no. 3, pp.pp. 1587-1592, July 2006.
**PDF** - W. Hendrickx, and T. Dhaene, “A discussion of “Rational approximation of frequency domain responses by vector fitting””, IEEE Power Engineering Society Letters. Accepted for publication.
- C.K. Sanathanan, and J. Koerner, “Transfer function synthesis as a ratio of two complex polynomials”, IEEE Trans. Automatic Control, vol. 8, no. 1, pp. 56-58, Jan. 1963.
- N. Wong and C. U. Lei, "IIR approximation of FIR filters via discrete-time vector fitting," IEEE Trans. Signal Processing, vol. 56, no. 3, pp.1296-1302, Mar 2008

Application of Vector Fitting:

Transmission line modeling

- K.M. Coperich, J. Morsey, V.I. Okhmatovski, A.C. Cangellaris and S.E. Ruehli, ”Systematic development of transmission-line models for interconnects with frequency-dependent losses”, IEEE Trans. Microwave Theory Tech., vol. 49, no. 10, pp. 1677-1685, Oct. 2001.
- K.M. Coperich, J. Morsey, A.C. Cangellaris and S.E. Ruehli, ”Physically consistent transmission line models for high-speed interconnects in lossy dielectrics”, IEEE Trans. Advanced Packaging, vol. 35, no. 2, pp. 129-135, May 2002.
- I.M. Elfadel, H.-M. Huang, A.E. Ruehli, A. Dounavis and M.S. Nakhla, "A comparative study of two transient analysis algorithms for lossy transmission lines with frequency-dependent data", IEEE Trans. Advanced Packaging, vol. 25, no. 2, pp. 143-153, May 2002.
- B. Gustavsen and A. Semlyen, "Simulation of transmission line transients using vector fitting and modal decomposition", IEEE Trans. Power Delivery, vol. 13, no. 2, pp. 605-614, April 1998. PDF
- B. Gustavsen and A. Semlyen, "Combined phase and modal domain calculation of transmission line transients based on vector fitting", IEEE Trans. Power Delivery, vol. 13, no. 2, pp. 596-604, April 1998.
**PDF** - B. Gustavsen, "Time delay identification for transmission line modeling", in Proc. Signal Processing on Interconnects, SPI 2004, to be published.
**PDF** - Er-Ping Li, En-Xiao Liu, Le-Wei Li and Mook-Seng Leong, ”A Coupled Efficient and Systematic Full-Wave Time-Domain Macromodeling and Circuit Simulation Method for Signal Integrity Analysis of High-Speed Interconnects”, IEEE Trans. Advanced Packaging, vol. 27, no. 1, pp. 213-223, Feb. 2004.
- E.-X. Liu, E.-P Liu and L.-W. Li, "Analysis of signal propagation on high-speed planar interconnect systems based on full-wave and macromodelling techniques", Microwave and Optical Technology Letters, vol. 39, no. 3, pp. 183-187, Nov. 2003.
- A.E. Ruehli, H-M. Huang and I.M. Elfadel, ”Transient analysis for lossy transmission lines using a method of characteristics based approach”, in Proc. Electrical Performance of Electronic Packaging 2002, pp. 367-370, 21-23 Oct. 2002.
- B. Zhong, S.L. Dvorak and J.L. Prince, "A new dispersive, hybrid phase-pole macromodel for frequency-dependent lossy transmission lines", In Proc. Electronic Component and Technlology Conference, may 27-30, pp. 1023-1027, 2003.

Terminal modeling based on Y-parameter responses

- M. Abdel-Rahman, A. Semlyen and M.R. Iravani, "Two-layer network equivalent for electromagnetic transients", IEEE Trans. Power Delivery, vol. 18, no. 4, pp. 1328-1335, October 2003.
- A. Antonini, ”Equivalent network synthesis for via holes discontinuities” IEEE Trans. Advanced Packaging, vol. 25, no. 4, pp. 528-536, Nov. 2002.
- A. Antonini, ”SPICE equivalent circuits of frequency-domain responses”, IEEE Trans. Electromagn. Compatibilty, vol. 45, no. 3, pp. 502-512, August 2003.
- S. Grivet-Talocia, ”Time-domain and frequency-domain macromodeling: Application to Package structures”, in Proc. IEEE Int. Symp. EMC 2003, Boston MA, pp. 570-574, August 18-22, 2003.
- B. Gustavsen, ”Application of vector fitting to high frequency transformer modeling”, in Proc. International Conference on Power System Transients, IPST’2003, New Orleans, paper 9d-2, Sept 28 - Oct 2, 2003.
**PDF** - B. Gustavsen, ”Wide band modeling of power transformers”, IEEE Trans. Power Delivery, vol. 19, no. 1, pp. 414-422, Jan. 2004.
**PDF** - B. Gustavsen, ”Frequency dependent modeling of power transformers with ungrounded windings”, IEEE Trans. Power Delivery, Vol. 19, no. 3, pp. 1328-1334, July 2004.
**PDF** - M.J. Manyahi and R. Thotappillil , "Transfer of lightning transients through distribution transformer circuits", in Proc. Internat. Conf. Lightning Protection 2002 (ICLP), Cracow, Poland, pp. 435-440, Sept. 2-6, 2002.
- D. Saraswat, R. Achar and M. Nakhla, ”Passive macromodels of microwave subnetworks characterized by measured/simulated data”, in Proc. Int. Microwave Symposium, IEEE MTT-S, vol. 2, pp. 999-1002, June 2003.

Terminal modeling based on S-parameter responses