A Class of Interpolating Positive Linear Operators: Theoretical and Computational Aspects

IEEE Trans. Microwave Theory Techn.

et al. 2013

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.

Section: ) Passive Parameterized Interpolationmentioning

confidence: 99%

Guaranteed Passive Parameterized Macromodeling by Using Sylvester State-Space Realizations

Samuel

Knockaert

IEEE Trans. Microwave Theory Techn.

et al. 2013

“…The parametrization step described in Section III-B uses positive interpolation operators [17] to parameterize frequency scaling coefficients, residues and directs terms. A rational model (14) can be seen as an interpolation of transfer functions with common poles.…”

Section: B Passivity Preserving Interpolationmentioning

confidence: 99%

Compact and Passive Parametric Macromodeling Using Reference Macromodels and Positive Interpolation Operators

IEEE Trans. Compon., Packag. Manufact. Technol.

Dhaene

Knockaert

2012

Abstract-We present an enhanced parametric macromodeling method that is able to generate compact and passive models over the entire design space of interest. It starts from a discrete set of data samples of the input-output system behavior (e.g. admittance, impedance and scattering parameters), which depend on multiple design variables such as layout and substrate parameters. The proposed approach generates accurate parametric macromodels whose size is not affected by the number of design parameters in addition to frequency. Stability and passivity are preserved over the design space of interest. Pertinent numerical results validate the proposed parametric macromodeling methods.

“…If scaling matrices are used instead of scaling coefficients , no particular condition has to be satisfied by . Multivariate interpolation schemes based on a class of positive interpolation operators [41] are used to parameterize . These schemes are able to guarantee the passivity of each scaled and frequency-shifted ROM by satisfying the properties (15a)-(15b).…”

Section: Multivariate Interpolationmentioning

confidence: 99%

Interpolation-Based Parameterized Model Order Reduction of Delayed Systems

IEEE Trans. Microwave Theory Techn.

Nakhla

Antonini

et al. 2012

Abstract-Three-dimensional electromagnetic methods are fundamental tools for the analysis and design of high-speed systems. These methods often generate large systems of equations, and model order reduction (MOR) methods are used to reduce such a high complexity. When the geometric dimensions become electrically large or signal waveform rise times decrease, time delays must be included in the modeling.Design space optimization and exploration are usually performed during a typical design process that consequently requires repeated simulations for different design parameter values. Efficient performing of these design activities calls for parameterized model order reduction (PMOR) methods, which are able to reduce large systems of equations with respect to frequency and other design parameters of the circuit, such as layout or substrate features.We propose a novel PMOR method for neutral delayed differential systems, which is based on an efficient and reliable combination of univariate model order reduction methods, a procedure to find scaling and frequency shifting coefficients and positive interpolation schemes. The proposed scaling and frequency shifting coefficients enhance and improve the modeling capability of standard positive interpolation schemes and allow accurate modeling of highly dynamic systems with a limited amount of initial univariate models in the design space. The proposed method is able to provide parameterized reduced order models passive by construction over the design space of interest. Pertinent numerical examples validate the proposed PMOR approach.Index Terms-Delayed systems, interpolation, parameterized model order reduction (PMOR), partial element equivalent circuit method (PEEC).