A Novel Framework for Parametric Loewner Matrix Interpolation

The generation of black-box macromodels of passive components at the chip, package, and board levels has become an important step of the electronic design automation (EDA) workflow. The vector fitting (VF) scheme is a very popular method for the extraction of such macromodels, and several multivariate extensions are now available for embedding external parameters in the model structure, thus enabling model-based variability analysis and design optimization. The Loewner matrix interpolation framework was recently suggested as an effective and promising alternative macromodeling approach to VF. In this article, we propose a parametric version of Loewner interpolation, which embeds orthogonal polynomials as an integral part of the parameterization framework. This approach is shown to be efficient and accurate and presents various advantages with respect to competing multivariate rational interpolation methods. These advantages include better control of model smoothness in the parameter space and a particularly efficient implementation of the singular value decomposition, which is the core of the model extraction scheme. These advantages are confirmed through several examples relevant for signal and power integrity applications.