# Matrix Fitting Toolbox

Matrix Fitting Toolbox contains a complete procedure for multi-port rational modeling from frequency domain data.. It is applicable to both Y-parameter and S-parameter data sets. Rational fitting and passivity enforcement is achieved by two subsequent function calls. The fitting procedure is based on vector fitting (vectfit3.m) while the passivity enforcement is based on perturbation of residue matrix eigenvalues with passivity assessment by half-size test matrices. A routine is avilable for generating netlist for ATP-EMTP.

This package (Matrix_Fitting_Toolbox_1.zip) contains Matlab routines for generating a multi-port rational model from tabulated data in the frequency domain. It is applicable to both Y-parameter and S-parameter data sets. It is intended to replace the previous mtrxfit.zip by offering superior computational speed and robustness.

## Download: matrix_fitting_toolbox_1.zip

- VFdriver.m calculates a rational model starting from a tabulated data (square matrix) in the frequency domain. It makes use of routine

vectfit3.m, also contained in the package. The returned result is a pole-residue model as well as the associated state-space model. The model has guaranteed stable poles. - RPdriver.m perturbs the model generated by VFdriver.m such that it becomes passive, by perturbing the eigenvalues of the its residue matrices. The model can represent both Y-parameter data and S-parameter data. The routine also takes care of the passivity assessment.

Restrictions of use:

- Embedding the program code in any commercial software is strictly prohibited.
- If the code is used in a scientific work, then reference should me made to the following publications:

VFdriver.m and vectfit3.m:

- 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. Link - B. Gustavsen, "
**Improving the pole relocating properties of vector fitting**", IEEE Trans. Power Delivery, vol. 21, no. 3, pp. 1587-1592, July 2006. Link - D. Deschrijver, M. Mrozowski, T. Dhaene, and D. De Zutter, “
**Macromodeling of Multiport Systems Using a Fast Implementation of the Vector Fitting Method**”, IEEE Microwave and Wireless Components Letters, vol. 18, no. 6, pp. 383-385, June 2008. Link

**RPdriver.m and FRP.m:**

- A. Semlyen and B. Gustavsen, “
**A half-size singularity test matrix for fast and reliable passivity assessment of rational models**”, IEEE Trans. Power Delivery, vol. 24, no. 1, pp. 345-351, January 2009. - B. Gustavsen, “
**Fast passivity enforcement for pole-residue models by perturbation of residue matrix eigenvalues**”, IEEE Trans. Power Delivery, vol. 23, no. 4, pp. 2278-2285, October 2008. - B. Gustavsen and A. Semlyen, “
**Fast passivity assessment for S-parameter rational models via a half-size test matrix**”, IEEE Trans. Microwave Theory And Techniques, vol. 56, no. 12, pp. 2701-2708, December 2008. - B. Gustavsen, “
**Fast passivity enforcement for S-parameter models by perturbation of residue matrix eigenvalues**”, IEEE Trans. Advanced Packaging, accepted.