Parametric macromodeling for S-parameter data based on internal nonexpansivity

We propose a novel parametric macromodeling method for systems described by scattering parameters, which depend on multiple design variables such as geometrical layout or substrate features. The new concept of internal nonexpansivity for bounded real systems is introduced. It is used in combination with suitable interpolation schemes to interpolate a set of state-space matrices, and hence poles and residues indirectly, to build accurate parametric macromodels. Stability and passivity are guaranteed by construction over the design space of interest. Pertinent numerical examples validate the proposed parametric macromodeling method.