Compact Parameterized Black-Box Modeling via Fourier-Rational Approximations

We present a novel black-box modeling approach for frequency responses that depend on additional parameters with periodic behavior. The methodology is appropriate for representing with compact low-order equivalent models the behavior of electromagnetic systems observed at well-defined ports and/or locations, including dependence on geometrical parameters with rotational symmetry. Examples can be polarization or incidence angles of a plane wave, or stirrer rotation in reverberation chambers. The proposed approach is based on fitting a Fourier-rational model to sampled frequency responses, where frequency dependence is represented through rational functions and parameter dependence through a Fourier series. Several examples from different applications are used to validate and demonstrate the approach.