Guaranteed Passive Parameterized Macromodeling by Using Sylvester State-Space Realizations

Abstract

Abstract-A novel state-space realization for parameterized macromodeling is proposed in this paper. A judicious choice of the state-space realization is required in order to account for the assumed smoothness of the state-space matrices with respect to the design parameters. This technique is used in combination with suitable interpolation schemes to interpolate a set of state-space matrices, and hence the poles and residues indirectly, in order to build accurate parameterized macromodels. The key points of the novel state-space realizations are the choice of a proper pivot matrix and a well-conditioned solution of a Sylvester equation. Stability and passivity are guaranteed by construction over the design space of interest. Pertinent numerical examples validate the proposed Sylvester realization for parameterized macromodeling.

Multivariate Adaptive Sampling of Parameterized Antenna Responses

“…In light of the above observation, the multivariate modeling of S-parameters can be accomplished by means of standard techniques from the parametric macromodeling literature [21]- [23]. These techniques however require the treatment of frequency as a special parameter, i.e., running EM simulations at multiple frequency points for each fixed geometry.…”

Parametric Modeling of Radiation Patterns and Scattering Parameters of Antennas

“…However, the interpolation of Gilbert state-space matrices may suffer from a non-smooth variation of the state-space matrices in the design space D, and this may lead to inaccurate results [11]. A more accurate parametric macromodel is obtained by converting the pole-residue transfer function in (14) into the barycentric form [13] as…”

“…Furthermore, in order to provide a full characterization of the antenna, a rational function representation, in pole-residue form, is utilized to model the antenna's S−parameters using the vector fitting (VF) method [17]. The poles and residues are then indirectly parameterized by first deriving a state-space realization of the rational function, followed by an appropriate similarity transform such that the variation of the state-space matrices is smooth over the design space [11]. The parametric models are generated from a limited set of EM simulations of the antenna under consideration.…”

Passive Parametric Macromodeling by Using Sylvester State-Space Realizations

“…This avoids the direct parameterization of poles and residues, when interpolating a set of state-space matrices in order to build a parametric macromodel. The present technique is able to deal accurately with bifurcation effects of poles and residues [6].…”