Vector Fitting
Brief description
Vector Fitting (VF) is a robust numerical method for rational approximation. It allows to identify state space models directly from measured/simulated (tabulated) data, both for single or multiple input/output systems. The resulting macromodel has guaranteed stable poles. Vector Fitting has been developed by Bjørn Gustavsen and Adam Semlyen in 1996. It has been successfully applied to a large number of modeling applications within power systems, highspeed interconnects, electronic packages, and microwave systems. SUMO Lab has contributed to the development of version 3 of the Vector Fitting code (vectfit3.m). It offers superior performance (in speed and memory consumption) for broadband macromodeling of large multiport systems due to a fast and accurate numerical implementation of the pole identification step.
Key features

Stable rational approximation: Vector Fitting [1] relocates the prescribed poles (of the rational partial fraction basis functions) of the macromodel until convergence, by solving a least squares problem iteratively. Pole flipping ensures stable poles. The pole identification step is followed by a residue identification step.

Improved convergence: A relaxed nontriviality constraint [2] is used in the pole identification step of VF for achieving faster convergence and less biasing.

Multiport structures: The sparse matrix structure of the linear least squares problem associated with the pole identification step is exploited to obtain superior modeling performance (in speed and memory consumption) [3].
Download instructions
The program code (vectfit3.m) is available at The Vector Fitting Web Site : ZIPfile
Restrictions of use:
If the code is used in a scientific work, then reference should be made to the following three publications:
 Rational approximation of frequency domain responses by Vector Fitting
B. Gustavsen, A. Semlyen,
IEEE Trans. Power Delivery, Vol. 14, No. 3, pp. 10521061, July 1999.  Improving the pole relocating properties of vector fitting
B. Gustavsen,
IEEE Trans. Power Delivery, Vol. 21, No. 3, pp. 15871592, July 2006.  Macromodeling of Multiport Systems using a Fast Implementation of the Vector Fitting Method
D. Deschrijver, M. Mrozowski, T. Dhaene, D. De Zutter,
IEEE Microwave and Wireless Components Letters, Vol. 18, No. 6, pp. 383385, June 2008.
 Rational approximation of frequency domain responses by Vector Fitting