# Complex 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 the Complex Vector Fitting code (*CVF*). The CVF technique extends the application of the baseband equivalent representation to RF and photonics analog devices, which are fundamental parts of modern communication systems (i.e. microwave filters are typically adopted in front-end circuits). A novel and robust Matlab implementation of the CVF modeling technique is presented here. The proposed toolbox allows one to define a comprehensive modeling framework for communication systems, where both digital and analog components can be represented and studied with the baseband equivalent representation.

## Key features

**Robust implementation**: the CVF toolbox relies on robust algorithms to compute a frequency-domain rational model of baseband scattering parameters, such as:- The relaxed formulation, improving the convergence performance;

- The fast QR step, speeding up calculations for multiport systems.

**Compact modeling method**: since poles and residues in CVF are not calculated as complex conjugate pairs, CVF is able to compute (indicatively) half-size models compared with state-of-the-art rational modeling methods, such as the Vector Fitting modeling technique.**Passivity enforcement**: passivity is a crucial property for time-domain simulation of baseband systems. The CVF toolbox includes robust routines for the passivity assessment and enforcement of the computed baseband models.

## Download instructions

The program code of Complex Vector Fitting is available as a ZIP-file

## Restrictions of use:

- Embedding any of (or parts from) the routines of the Complex Vector Fitting toolbox in a commercial software, or a software requiring licensing, is strictly prohibited. This applies to all routines.
- If the code is used in a
*scientific work*, then reference should be made to the following two publications: -
**Time-domain Compact Macromodeling of Linear Photonic Circuits via Complex Vector Fitting**

Y. Ye, D. Spina, D. Deschrijver, W. Bogaerts, and T. Dhaene,

Photonics Research, vol. 7, no. 7, pp. 771-782, July 2019.**Complex Vector Fitting toolbox: a Software Package for the Modeling and Simulation of General Linear and Passive Baseband Systems**

D. Spina, Y. Ye, D. Deschrijver, W. Bogaerts and T. Dhaene,

Electronics Letters, vol. 57, no. 10, pp. 404-406, May 2021.

- The Matrix Fitting Toolbox is required for the code here provided to run correctly.

The toolbox is not included in this distribution, but it can be downloaded at this website. Please, check also the necessary references to be made when using the Matrix Fitting Toolbox in a scientific work.