Orthonormal Vector

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Tom Dhaene - One of the best experts on this subject based on the ideXlab platform.

  • Accurate macromodeling algorithm for time domain identification of transient port responses
    International Journal of Numerical Modelling-electronic Networks Devices and Fields, 2011
    Co-Authors: Dirk Deschrijver, Tom Dhaene
    Abstract:

    SUMMARY Orthonormal Vector fitting is a robust method for broadband macromodeling of frequency domain responses. The use of Orthonormal rational basis functions makes the conditioning of the system equations less sensitive to the initial pole specification when compared with the classical Vector Fitting procedure. This paper presents a time domain generalization of the technique to compute broadband rational macromodels from transient input–output port responses. The efficacy of the approach is illustrated by two numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.

  • data driven parameterized model order reduction using z domain multivariate Orthonormal Vector fitting technique
    Workshop on Model Reduction for Circuit Simulation, 2011
    Co-Authors: Francesco Ferranti, Luc Knockaert, Dirk Deschrijver, Tom Dhaene
    Abstract:

    Efficient real-time design space exploration, design optimization and sensitivity analysis call for Parameterized Model Order Reduction (PMOR) techniques to take into account several design parameters, such as geometrical layout or substrate characteristics, in addition to time or frequency. This chapter presents a robust multivariate extension of the z-domain Orthonormal Vector Fitting technique. The new method provides accurate and compact rational parametric macromodels based on numerical electromagnetic simulations or measurements in either frequency-domain or time-domain. The technique can be seen as a data-driven PMOR method.

  • Parametric Macromodeling of Lossy and Dispersive Multiconductor Transmission Lines
    IEEE Transactions on Advanced Packaging, 2010
    Co-Authors: Francesco Ferranti, Tom Dhaene, Giulio Antonini, Luc Knockaert
    Abstract:

    We propose an innovative parametric macromodeling technique for lossy and dispersive multiconductor transmission lines (MTLs) that can be used for interconnect modeling. It is based on a recently developed method for the analysis of lossy and dispersive MTLs extended by using the multivariate Orthonormal Vector fitting (MOVF) technique to build parametric macromodels in a rational form. They take into account design parameters, such as geometrical layout or substrate features, in addition to frequency. The presented technique is suited to generate state-space models and synthesize equivalent circuits, which can be easily embedded into conventional SPICE-like solvers. Parametric macromodels allow to perform design space exploration, design optimization, and sensitivity analysis efficiently. Numerical examples validate the proposed approach in both frequency and time domain.

  • Parameterized models for crosstalk analysis in high-speed interconnects
    2009 IEEE International Symposium on Electromagnetic Compatibility, 2009
    Co-Authors: Francesco Ferranti, Luc Knockaert, Tom Dhaene, Giulio Antonini
    Abstract:

    We present a new parametric macromodeling technique for lossy and dispersive multiconductor transmission lines (MTLs), that is suitable to interconnect modeling. It is based on a recently introduced spectral approach for the analysis of lossy and dispersive MTLs extended by utilizing the Multivariate Orthonormal Vector Fitting (MOVF) technique to build parametric macromodels in a rational form. They can handle design parameters, such as substrate or geometrical layout features, in addition to frequency. The presented technique is suited to generate state-space models and synthesize equivalent circuits, which can be easily embedded into conventional SPICE-like solvers. Parametric macromodels allow to carry out design space exploration, design optimization and crosstalk analysis efficiently. A numerical example validates the proposed approach in both frequency and time domain and is focused on the crosstalk analysis.

  • Parameterized macromodels of multiconductor transmission lines
    2009 IEEE Workshop on Signal Propagation on Interconnects, 2009
    Co-Authors: Giulio Antonini, Francesco Ferranti, Tom Dhaene, Luc Knockaert
    Abstract:

    We introduce a novel parametrization scheme for lossy and dispersive multiconductor transmission lines (MTLs) having a cross-section depending on geometrical and physical parameters, that is suitable to interconnect modeling. The proposed approach is based on the dyadic Green's function method for the analysis of lossy and dispersive MTLs which is parameterized by using the Multivariate Orthonormal Vector Fitting (MOVF) technique to build parametric macromodels in a rational form. Design parameters, such as substrate or geometrical layout features, in addition to frequency, can be easily handled. The rational form of the multi-port macromodel describing the MTL is a direct consequence of the MOVF technique and is especially suited to generate state-space macromodels or to be synthesized into equivalent circuits, which can be easily embedded into conventional SPICE-like solvers. A numerical example is presented providing evidence of the accuracy of the proposed approach in both frequency and time-domain.

Dirk Deschrijver - One of the best experts on this subject based on the ideXlab platform.

  • Accurate macromodeling algorithm for time domain identification of transient port responses
    International Journal of Numerical Modelling-electronic Networks Devices and Fields, 2011
    Co-Authors: Dirk Deschrijver, Tom Dhaene
    Abstract:

    SUMMARY Orthonormal Vector fitting is a robust method for broadband macromodeling of frequency domain responses. The use of Orthonormal rational basis functions makes the conditioning of the system equations less sensitive to the initial pole specification when compared with the classical Vector Fitting procedure. This paper presents a time domain generalization of the technique to compute broadband rational macromodels from transient input–output port responses. The efficacy of the approach is illustrated by two numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.

  • data driven parameterized model order reduction using z domain multivariate Orthonormal Vector fitting technique
    Workshop on Model Reduction for Circuit Simulation, 2011
    Co-Authors: Francesco Ferranti, Luc Knockaert, Dirk Deschrijver, Tom Dhaene
    Abstract:

    Efficient real-time design space exploration, design optimization and sensitivity analysis call for Parameterized Model Order Reduction (PMOR) techniques to take into account several design parameters, such as geometrical layout or substrate characteristics, in addition to time or frequency. This chapter presents a robust multivariate extension of the z-domain Orthonormal Vector Fitting technique. The new method provides accurate and compact rational parametric macromodels based on numerical electromagnetic simulations or measurements in either frequency-domain or time-domain. The technique can be seen as a data-driven PMOR method.

  • robust parametric macromodeling using multivariate Orthonormal Vector fitting
    IEEE Transactions on Microwave Theory and Techniques, 2008
    Co-Authors: Dirk Deschrijver, Tom Dhaene, D De Zutter
    Abstract:

    A robust multivariate extension of the Orthonormal Vector fitting technique is introduced for rational parametric macromodeling of highly dynamic responses in the frequency domain. The technique is applicable to data that is sparse or dense, deterministic or a bit noisy, and grid-based or scattered in the design space. For a specified geometrical parameter combination, a SPICE equivalent model can be calculated.

  • Efficient Time-Domain Macromodeling of Complex Interconnection Structures
    EUROCON 2007 - The International Conference on "Computer as a Tool", 2007
    Co-Authors: B Haegeman, Dirk Deschrijver, Tom Dhaene
    Abstract:

    The Vector fitting algorithm is an iterative procedure to compute rational approximations of frequency-domain responses. It was shown that the robustness of this technique can be enhanced by using a set of Orthonormal rational basis functions, leading to the Orthonormal Vector fitting method. In this paper, a time-domain implementation of this method is proposed for the macromodeling of transient port responses. It is shown that this method is more robust towards the initial pole specification, when compared to the classical time-domain Vector Fitting method [3].

  • Advancements in Iterative Methods for Rational Approximation in the Frequency Domain
    IEEE Transactions on Power Delivery, 2007
    Co-Authors: Dirk Deschrijver, Bjørn Gustavsen, Tom Dhaene
    Abstract:

    Rational approximation of frequency-domain responses is commonly used in electromagnetic transients programs for frequency-dependent modeling of transmission lines and to some extent, network equivalents (FDNEs) and transformers. This paper analyses one of the techniques [Vector fitting (VF)] within a general iterative least-squares scheme that also explains the relation with the polynomial-based Sanathanan-Koerner iteration. Two recent enhancements of the original VF formulation are described: Orthonormal Vector fitting (OVF) which uses Orthonormal functions as basis functions instead of partial fractions, and relaxed Vector fitting (RVF), which uses a relaxed least-squares normalization for the pole identification step. These approaches have been combined into a single approach: relaxed Orthonormal Vector fitting (ROVF). The application to FDNE identification shows that ROVF offers more robustness and better convergence than the original VF formulation. Alternative formulations using explicit weighting and total least squares are also explored.

D De Zutter - One of the best experts on this subject based on the ideXlab platform.

  • robust parametric macromodeling using multivariate Orthonormal Vector fitting
    IEEE Transactions on Microwave Theory and Techniques, 2008
    Co-Authors: Dirk Deschrijver, Tom Dhaene, D De Zutter
    Abstract:

    A robust multivariate extension of the Orthonormal Vector fitting technique is introduced for rational parametric macromodeling of highly dynamic responses in the frequency domain. The technique is applicable to data that is sparse or dense, deterministic or a bit noisy, and grid-based or scattered in the design space. For a specified geometrical parameter combination, a SPICE equivalent model can be calculated.

James H Burge - One of the best experts on this subject based on the ideXlab platform.

  • Orthonormal Vector polynomials in a unit circle application fitting mapping distortions in a null test
    Proceedings of SPIE, 2009
    Co-Authors: Chunyu Zhao, James H Burge
    Abstract:

    We developed a complete and Orthonormal set of Vector polynomials defined over a unit circle. One application of these Vector polynomials is for fitting the mapping distortions in an interferometric null test. This paper discusses the source of the mapping distortions and the approach of fitting the mapping relations, and justifies why the set of Vector polynomials is the appropriate choice for this purpose. Examples are given to show the excellent fitting results with the polynomials.

  • Orthonormal Vector polynomials in a unit circle part ii completing the basis set
    Optics Express, 2008
    Co-Authors: Chunyu Zhao, James H Burge
    Abstract:

    Zernike polynomials provide a well known, orthogonal set of scalar functions over a circular domain, and are commonly used to represent wavefront phase or surface irregularity. A related set of orthogonal functions is given here which represent Vector quantities, such as mapping distortion or wavefront gradient. Previously, we have developed a basis of functions generated from gradients of Zernike polynomials. Here, we complete the basis by adding a complementary set of functions with zero divergence – those which are defined locally as a rotation or curl.

  • Orthonormal Vector polynomials in a unit circle part i basis set derived from gradients of zernike polynomials
    Optics Express, 2007
    Co-Authors: Chunyu Zhao, James H Burge
    Abstract:

    Zernike polynomials provide a well known, orthogonal set of scalar functions over a circular domain, and are commonly used to represent wavefront phase or surface irregularity. A related set of orthogonal functions is given here which represent Vector quantities, such as mapping distortion or wavefront gradient. These functions are generated from gradients of Zernike polynomials, made Orthonormal using the Gram-Schmidt technique. This set provides a complete basis for representing Vector fields that can be defined as a gradient of some scalar function. It is then efficient to transform from the coefficients of the Vector functions to the scalar Zernike polynomials that represent the function whose gradient was fit. These new Vector functions have immediate application for fitting data from a Shack-Hartmann wavefront sensor or for fitting mapping distortion for optical testing. A subsequent paper gives an additional set of Vector functions consisting only of rotational terms with zero divergence. The two sets together provide a complete basis that can represent all Vector distributions in a circular domain.

Luc Knockaert - One of the best experts on this subject based on the ideXlab platform.

  • data driven parameterized model order reduction using z domain multivariate Orthonormal Vector fitting technique
    Workshop on Model Reduction for Circuit Simulation, 2011
    Co-Authors: Francesco Ferranti, Luc Knockaert, Dirk Deschrijver, Tom Dhaene
    Abstract:

    Efficient real-time design space exploration, design optimization and sensitivity analysis call for Parameterized Model Order Reduction (PMOR) techniques to take into account several design parameters, such as geometrical layout or substrate characteristics, in addition to time or frequency. This chapter presents a robust multivariate extension of the z-domain Orthonormal Vector Fitting technique. The new method provides accurate and compact rational parametric macromodels based on numerical electromagnetic simulations or measurements in either frequency-domain or time-domain. The technique can be seen as a data-driven PMOR method.

  • Parametric Macromodeling of Lossy and Dispersive Multiconductor Transmission Lines
    IEEE Transactions on Advanced Packaging, 2010
    Co-Authors: Francesco Ferranti, Tom Dhaene, Giulio Antonini, Luc Knockaert
    Abstract:

    We propose an innovative parametric macromodeling technique for lossy and dispersive multiconductor transmission lines (MTLs) that can be used for interconnect modeling. It is based on a recently developed method for the analysis of lossy and dispersive MTLs extended by using the multivariate Orthonormal Vector fitting (MOVF) technique to build parametric macromodels in a rational form. They take into account design parameters, such as geometrical layout or substrate features, in addition to frequency. The presented technique is suited to generate state-space models and synthesize equivalent circuits, which can be easily embedded into conventional SPICE-like solvers. Parametric macromodels allow to perform design space exploration, design optimization, and sensitivity analysis efficiently. Numerical examples validate the proposed approach in both frequency and time domain.

  • Parameterized models for crosstalk analysis in high-speed interconnects
    2009 IEEE International Symposium on Electromagnetic Compatibility, 2009
    Co-Authors: Francesco Ferranti, Luc Knockaert, Tom Dhaene, Giulio Antonini
    Abstract:

    We present a new parametric macromodeling technique for lossy and dispersive multiconductor transmission lines (MTLs), that is suitable to interconnect modeling. It is based on a recently introduced spectral approach for the analysis of lossy and dispersive MTLs extended by utilizing the Multivariate Orthonormal Vector Fitting (MOVF) technique to build parametric macromodels in a rational form. They can handle design parameters, such as substrate or geometrical layout features, in addition to frequency. The presented technique is suited to generate state-space models and synthesize equivalent circuits, which can be easily embedded into conventional SPICE-like solvers. Parametric macromodels allow to carry out design space exploration, design optimization and crosstalk analysis efficiently. A numerical example validates the proposed approach in both frequency and time domain and is focused on the crosstalk analysis.

  • Parameterized macromodels of multiconductor transmission lines
    2009 IEEE Workshop on Signal Propagation on Interconnects, 2009
    Co-Authors: Giulio Antonini, Francesco Ferranti, Tom Dhaene, Luc Knockaert
    Abstract:

    We introduce a novel parametrization scheme for lossy and dispersive multiconductor transmission lines (MTLs) having a cross-section depending on geometrical and physical parameters, that is suitable to interconnect modeling. The proposed approach is based on the dyadic Green's function method for the analysis of lossy and dispersive MTLs which is parameterized by using the Multivariate Orthonormal Vector Fitting (MOVF) technique to build parametric macromodels in a rational form. Design parameters, such as substrate or geometrical layout features, in addition to frequency, can be easily handled. The rational form of the multi-port macromodel describing the MTL is a direct consequence of the MOVF technique and is especially suited to generate state-space macromodels or to be synthesized into equivalent circuits, which can be easily embedded into conventional SPICE-like solvers. A numerical example is presented providing evidence of the accuracy of the proposed approach in both frequency and time-domain.

  • a multivariate Orthonormal Vector fitting based estimation technique
    IFAC Proceedings Volumes, 2009
    Co-Authors: Francesco Ferranti, Y Rolain, Koen Vandermot, Luc Knockaert, Tom Dhaene
    Abstract:

    Abstract This paper modifies a recent robust parametric macromodeling technique called Multivariate Orthonormal Vector Fitting (MOVF), to handle noisy data in an output error estimation framework. The new method provides accurate and compact rational parametric macromodels based on measurements in the frequency domain. The performance of the multivariate method is shown on simulation as well as on real measurements.