Compact Parameterized Black-Box Modeling via Fourier-Rational Approximations

Abstract

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.

A Perturbation Scheme for Passivity Verification and Enforcement of Parameterized Macromodels

“…where the basis functions ξ ℓ (ϑ) are responsible for reproducing the variations induced by the external parameter ϑ. We remark that the adopted model structure is the same as discussed in [1] and originally introduced in [32], [36], [37], [39], [40], where polynomials, piecewise polynomials, or trigonometric polynomials were used as basis functions ξ ℓ . This work makes no a-priori assumption on the specific choice of basis functions, which should be defined considering the particular application at hand.…”

Accurate Characterization of Reverberation Chamber Resonant Modes From Scattering Parameters Measurement

“…The accuracy of a pole extraction process is directly related to the method used to compute the mode properties from the S 21 parameter, each pole being related to a resonant mode. Several methods have been proposed, either in the time-domain or in the frequency domain, to extract the poles and their related residues: Prony [16], Matrix Pencil (MP) [17]- [21], Cauchy [22], Vector Fitting [23]- [25], Harmonic Inversion [26]- [28] and others. These methods are based on different approaches but they all require at some point to indicate the number of poles N to be extracted.…”

“…However, this overestimation also implies the extraction of many spurious poles that need to be filtered out. One way (as in [25]) is based on the assumption of the mode continuity versus stirrer rotation. It requires to track the mode variation as a function of the stirrer rotation and to delete the modes that are extracted randomly for specific stirrer positions.…”

Parameterized macromodels for EMC/EMI simulation of electrical interconnects

“…The above phenomena are best captured through a full-wave characterization of the signal transmission system, defined at suitable electrical ports where transmitters and receivers are located. In addition, some electromagnetic ports are needed to account for the possible presence of incident fields [1,2]. The objective of this work is to construct behavioral, reduced-order interconnect models that can account for external field excitation, and that can be simulated in time-domain for Signal Integrity analyses using standard ODE or circuit (SPICE) solvers.…”

“…We approach the above problem by fitting a parameterized macromodel with rational transfer function and parameter-dependent coefficients to a set frequency (scattering) responses obtained by * Dipartimento di Elettronica e Telecomunicazioni, Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Torino, Italy, e-mail: stefano.grivet@polito.it, tel. : +39 011 0904104 a field solver [4,5], suitably generalized to account for the electromagnetic ports [2]. The model is identified through a parameterized Generalized Sanathanan-Koerner iteration [2,5], and model stability and passivity are checked and enforced based on structured perturbation [6,7].…”