Full-wave PEEC time-domain method for the modeling of on-chip interconnects

2010 IEEE International Symposium on Electromagnetic Compatibility

Dhaene

Knockaert

et al. 2010

Abstract-We present a novel parameterized model order reduction technique applicable to the Partial Element EquivalentCircuit analysis that provides parametric reduced order models, stable and passive by construction, over a user defined design space. We treat the construction of parametric reduced order models on scattered design space grids. This new parameterized model order reduction technique is based on the hybridization of traditional passivity-preserving model order reduction methods and interpolation schemes based on a class of positive interpolation operators, in order to guarantee overall stability and passivity of the parametric reduced order model. Pertinent numerical examples validate the proposed approach.

Section: Peec Formulationmentioning

confidence: 99%

Parameterized model order reduction with guaranteed passivity for PEEC Circuit analysis

2010 IEEE International Symposium on Electromagnetic Compatibility

Dhaene

Knockaert

et al. 2010

“…The PEEC method uses a circuit interpretation of the Electric Field Integral Equation (EFIE) and it is especially suitable to problems involving both electromagnetic fields and circuits. To generate the NDDE systems used in the numerical examples, we have used a PEEC formulation which includes delay elements, called PEEC method [7,12].…”

Section: Nddesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Simply using rational models can result in significant errors and artifacts. Therefore, systems of neutral delayed differential equations (NDDE) [7] becomes fundamental to accurately describe the behavior of such structures.Traditional MOR techniques perform model reduction only with respect to frequency, but a typical design process includes design space optimization and exploration, and thus it requires repeated simulations for different design parameter values (e.g. geometrical layout or substrate characteristics).…”

mentioning

confidence: 99%

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Parameterized model order reduction of delayed systems using an interpolation approach with amplitude and frequency scaling coefficients

2012 IEEE 16th Workshop on Signal and Power Integrity (SPI)

Nakhla

Antonini

et al. 2012

When the geometric dimensions become electrically large or signal waveform rise times decrease, time delays must be included in the modeling. We present an innovative PMOR technique for neutral delayed differential systems, which is based on an efficient and reliable combination of univariate model order reduction methods, amplitude and frequency scaling coefficients and positive interpolation schemes. It 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. IntroductionComplex high-speed systems require 3-D electromagnetic (EM) methods [1,2] as analysis and design tools. Large systems of equations are usually generated by the use of these methods and model order reduction (MOR) techniques are crucial to reduce the complexity of EM models and the computational cost of the simulations, while retaining the important physical features of the original system [3,4]. Over the last years, the development of methods to build reduced order models (ROMs) of EM systems has been intensively investigated, with applications to interconnects, vias and high-speed packages [5,6].When signal waveform rise times decrease and the corresponding frequency content increases or the geometric dimensions become electrically large, time delays must be taken into account and included in the modeling. Simply using rational models can result in significant errors and artifacts. Therefore, systems of neutral delayed differential equations (NDDE) [7] becomes fundamental to accurately describe the behavior of such structures.Traditional MOR techniques perform model reduction only with respect to frequency, but a typical design process includes design space optimization and exploration, and thus it requires repeated simulations for different design parameter values (e.g. geometrical layout or substrate characteristics). Such design activities call for parameterized model order reduction (PMOR) methods that can reduce large systems of equations with respect to frequency and other design parameters.Over the years, a limited number of PMOR methods for NDDE systems have been developed [8][9][10]. They are mainly

“…Among all EM methods, the Partial Element Equivalent Circuit (PEEC) method [2] uses a circuit interpretation of the Electric Field Integral Equation (EFIE) [5], therefore it is especially suitable to problems involving both electromagnetic fields and circuits [2], [6]. If we consider a quasi-static PEEC formulation [2], which approximates the fullwave PEEC approach [7], an equivalent RLC circuit is obtained, since the time delays between the elements in the full-wave PEEC formulation are neglected. Systems of ordinary differential equations (ODE) are obtained.…”

Section: Introductionmentioning

confidence: 99%

Reduced order modeling of delayed PEEC circuits

2011 IEEE MTT-S International Microwave Symposium

Nakhla

Antonini

et al. 2011

Abstract-We propose a novel model order reduction technique that is able to accurately reduce electrically large systems with delay elements, which can be described by means of neutral delayed differential equations. It is based on an adaptive multipoint expansion and model order reduction of equivalent first order systems. The neutral delayed differential formulation is preserved in the reduced model. Pertinent numerical results validate the proposed model order reduction approach.Index Terms-Delayed Partial Element Equivalent Circuit method, reduced order systems, neutral delayed differential equations.