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Interpolation-based parameterized model order reduction of delayed systems

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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.
Keywords
SIMULATION, APPROXIMATION, CIRCUIT MODELS, EFFICIENT, TIME-DOMAIN, HIGH-SPEED INTERCONNECTS, WAVE-FORM EVALUATION, FORMULATION, NETWORKS, ARNOLDI, Delayed systems, interpolation, parameterized model order reduction (PMOR), partial element equivalent circuit method (PEEC)

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Please use this url to cite or link to this publication:

Chicago
Ferranti, Francesco, Michel Nakhla, Giulio Antonini, Tom Dhaene, Luc Knockaert, and Albert E Ruehli. 2012. “Interpolation-based Parameterized Model Order Reduction of Delayed Systems.” Ieee Transactions on Microwave Theory and Techniques 60 (3): 431–440.
APA
Ferranti, F., Nakhla, M., Antonini, G., Dhaene, T., Knockaert, L., & Ruehli, A. E. (2012). Interpolation-based parameterized model order reduction of delayed systems. IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, 60(3), 431–440.
Vancouver
1.
Ferranti F, Nakhla M, Antonini G, Dhaene T, Knockaert L, Ruehli AE. Interpolation-based parameterized model order reduction of delayed systems. IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. 2012;60(3):431–40.
MLA
Ferranti, Francesco, Michel Nakhla, Giulio Antonini, et al. “Interpolation-based Parameterized Model Order Reduction of Delayed Systems.” IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 60.3 (2012): 431–440. Print.
@article{3004061,
  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.},
  author       = {Ferranti, Francesco and Nakhla, Michel and Antonini, Giulio and Dhaene, Tom and Knockaert, Luc and Ruehli, Albert E},
  issn         = {0018-9480},
  journal      = {IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES},
  keyword      = {SIMULATION,APPROXIMATION,CIRCUIT MODELS,EFFICIENT,TIME-DOMAIN,HIGH-SPEED INTERCONNECTS,WAVE-FORM EVALUATION,FORMULATION,NETWORKS,ARNOLDI,Delayed systems,interpolation,parameterized model order reduction (PMOR),partial element equivalent circuit method (PEEC)},
  language     = {eng},
  number       = {3},
  pages        = {431--440},
  title        = {Interpolation-based parameterized model order reduction of delayed systems},
  url          = {http://dx.doi.org/10.1109/TMTT.2011.2181858},
  volume       = {60},
  year         = {2012},
}

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