Elizabeth Rita Samuel

Guaranteed Passive Parameterized Macromodeling by Using Sylvester State-Space Realizations

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.

Model Order Reduction of Time-Delay Systems Using a Laguerre Expansion Technique

The demands for miniature sized circuits with higher operating speeds have increased the complexity of the circuit, while at high frequencies it is known that effects such as crosstalk, attenuation and delay can have adverse effects on signal integrity. To capture these high speed effects a very large number of system equations is normally required and hence model order reduction techniques are required to make the simulation of the circuits computationally feasible. This paper proposes a higher order Krylov subspace algorithm for model order reduction of time-delay systems based on a Laguerre expansion technique. The proposed technique consists of three sections i.e., first the delays are approximated using the recursive relation of Laguerre polynomials, then in the second part, the reduced order is estimated for the time-delay system using a delay truncation in the Laguerre domain and in the third part, a higher order Krylov technique using Laguerre expansion is computed for obtaining the reduced order time-delay system. The proposed technique is validated by means of real world numerical examples.

Matrix-Interpolation-Based Parametric Model Order Reduction for Multiconductor Transmission Lines With Delays

A novel parametric model order reduction technique based on matrix interpolation for multiconductor transmission lines (MTLs) with delays having design parameter variations is proposed in this brief. Matrix interpolation overcomes the oversize problem caused by input-output system-level interpolation-based parametric macromodels. The reduced state-space matrices are obtained using a higher-order Krylov subspace-based model order reduction technique, which is more efficient in comparison to the Gramian-based parametric modeling in which the projection matrix is computed using a Cholesky factorization. The design space is divided into cells, and then the Krylov subspaces computed for each cell are merged and then truncated using an adaptive truncation algorithm with respect to their singular values to obtain a compact common projection matrix. The resulting reduced-order state-space matrices and the delays are interpolated using positive interpolation schemes, making it computationally cheap and accurate for repeated system evaluations under different design parameter settings. The proposed technique is successfully applied to RLC (R-resistor, L-inductor, C-capacitance) and MTL circuits with delays.

Passivity-Preserving Parameterized Model Order Reduction Using Singular Values and Matrix Interpolation

We present a parameterized model order reduction method based on singular values and matrix interpolation. First, a fast technique using grammians is utilized to estimate the reduced order, and then common projection matrices are used to build parameterized reduced order models (ROMs). The design space is divided into cells, and a Krylov subspace is computed for each cell vertex model. The truncation of the singular values of the merged Krylov subspaces from the models located at the vertices of each cell yields a common projection matrix per design space cell. Finally, the reduced system matrices are interpolated using positive interpolation schemes to obtain a guaranteed passive parameterized ROM. Pertinent numerical results validate the proposed technique.

Parametric Modeling of Radiation Patterns and Scattering Parameters of Antennas

This paper describes a data-driven method to model the radiation patterns (over a large angular region) and scattering parameters of antennas as a function of the geometry of the antenna. The radiation pattern model consists of a linear combination of characteristic basis function patterns (CBFPs), where the expansion coefficients of the CBFPs are the functions of geometrical features of the antenna. Scattering parameters are modeled by means of parameterized state-space matrices. The obtained models are quick to evaluate and are thus suitable for design activities where multiple simulations are required. The proposed method is validated through illustrative examples.

Multipoint Model Order Reduction Using Reflective Exploration

Reduced order models obtained by model order reduction methods must be accurate over the whole frequency range of interest. Multipoint reduction algorithms allow to generate accurate reduced models. In this paper, we propose the use of a reflective exploration technique for obtaining the expansion points adaptively for the reduction algorithm. At each expansion point the corresponding projection matrix is computed. Then, the projection matrices are merged and truncated based on their singular values to obtain a compact reduced order model. Three conductor transmission line example is used to illustrate the technique.

RATIONAL MODELING OF MULTIVARIATE MULTI-FIDELITY DATA

Abstract. Accurate multi-fidelity modeling is of high importance in the present day engineering design process. It allows to model computationally expensive simulations at a reduced cost by combining simulations with variable fidelity levels. In this paper, a novel algorithm is proposed to build multivariate models from variable fidelity simulations using rational functions. The modeling is based on high-fidelity data and low-fidelity data that is sampled over a parameter space of interest. The former is assumed to be computationally expensive and sparse, whereas the latter is cheaper to obtain but comes at a lower accuracy. It is shown that accurate rational models can be built at a reduced cost by combining these types of data. The effectiveness of the algorithm is applied to several examples and confirmed by numerical results.

Passive parametric macromodeling by using Sylvester state-space realizations

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. The direct parameterization of poles and residues may be not appropriate, due to their possible non-smooth behavior with respect to design parameters. This is avoided in the proposed technique, by converting the pole-residue description to a Sylvester description which is computed for each root macromodel. This technique is used in combination with suitable parameterizing schemes for interpolating a set of state-space matrices, and hence the poles and residues indirectly, in order to build accurate parametric macromodels. The key features of the present approach are first the choice of a proper pivot matrix and second, finding 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 technique for parametric macromodeling.

Multipoint model order reduction for systems with delays

An adaptive frequency sampling algorithm is proposed in this paper to automate the generation of reduced order models for systems with delays which can be represented as frequency dependent state-space matrices. Reflective exploration technique is used to obtain an optimum number of frequency samples for which the reduced state-space matrices per frequency is computed using a common projection matrix and is then interpolated to obtain the frequency response. The algorithm is illustrated using a numerical example.

Passivity preserving multipoint model order reduction using reflective exploration

Reduced state-space models obtained by model order reduction methods must be accurate over the whole frequency range of interest and must also preserve passivity. In this paper, we propose multipoint reduction technique using reflective exploration for adaptively choosing the expansion points. The projection matrices obtained from the expansion points are merged to form the overall projection matrix. In order to obtain a more compact model the projection matrix is truncated based on its singular values. Finally, the reduced order model is obtained, while ensuring that the passivity of the reduced system is preserved during the reduction process.