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, high-speed 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 non-triviality constraint [2] is used in the pole identification step of VF for achieving faster convergence and less biasing.

  • Multi-port 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 : ZIP-file

Restrictions of use:

If the code is used in a scientific work, then reference should be made to the following three publications:
    1. Rational approximation of frequency domain responses by Vector Fitting pdf
      B. Gustavsen, A. Semlyen,
      IEEE Trans. Power Delivery, Vol. 14, No. 3, pp. 1052-1061, July 1999.
    2. Improving the pole relocating properties of vector fitting pdf
      B. Gustavsen,
      IEEE Trans. Power Delivery, Vol. 21, No. 3, pp. 1587-1592, July 2006.
    3. Macromodeling of Multiport Systems using a Fast Implementation of the Vector Fitting Method pdf
      D. Deschrijver, M. Mrozowski, T. Dhaene, D. De Zutter,
      IEEE Microwave and Wireless Components Letters, Vol. 18, No. 6, pp. 383-385, June 2008.