During a typical design process of electromagnetic (EM) systems, design space exploration, design optimization, and sensitivity analysis are usually performed, and this requires multiple simulations for different design parameter values (e.g., layout features). Parameterized macromodels are valuable tools to efficiently and accurately perform these design activities, while avoiding new measurements or simulations for each new parameter configuration. Parameterized macromodels are multivariate models that describe the complex behavior of EM systems, typically characterized by frequency (or time) and several geometrical and physical design parameters, such as layout or substrate features. Parameterized macromodeling techniques able to guarantee overall stability and passivity are based on the interpolation of a set of univariate macromodels, called root macromodels. This interpolation process of input-output systems leads to parameterization of the residues, but unfortunately not of the poles. Passive interpolation of the state-space matrices of a set of root macromodels provides an increased modeling capability with respect to input-output interpolation. Unfortunately, these methods are sensitive to issues related to the interpolation of state-space matrices, such as the smoothness of the state-space matrices as a function of the parameters. In this talk, I would like to introduce a novel state-space realization that is suitable to build accurate parameterized macromodels. The direct parameterization of poles and residues is avoided, due to their potentially non-smooth behavior with respect to the design parameters. The Vector Fitting (VF) technique is initially used to build a set of root macromodel for different combinations of design variables. Stability for each root macromodel is enforced by pole flipping , while passivity is checked and enforced. A conversion from a pole-residue form obtained by means of VF to a Sylvester realization is computed for each root macromodel. The key points of the Sylvester realization is the choice of a pivot or reference matrix and the obtention of a well-conditioned solution to the Sylvester equation. Since the same pivot matrix is used for all state-space realizations of the root macromodels, smooth variations of the state-space matrices with respect to the design parameters can be expected.
Elizabeth Rita Samuel obtained her PhD in electrical engineering from Gent University, Belgium in 2015. She had completed her M.Tech in Guidance Navigation and Control and B.Tech in Electrical and Electronics Engineering from Kerala University. She has a teaching experience of two and a half years in different engineering institutions in Kerala. Also has worked as a programmer analyst for CTS for almost two years for a project with 3M Europe. The topic of her dissertation for PhD was Parameterized Modeling and Model Order Reduction for Large Electrical Systems. She has 4 international journal papers and 8 international conference proceedings published.