Efficient design optimization of complex electromagnetic systems using parametric macromodeling techniques

We propose a new parametric macromodeling technique for complex electromagnetic systems described by scattering parameters, which are parameterized by multiple design variables such as layout or substrate feature. The proposed technique is based on an efficient and reliable combination of rational identification, a procedure to find scaling and frequency shifting system coefficients, and positive interpolation schemes. Parametric macromodels can be used for efficient and accurate design space exploration and optimization. A design optimization example for a complex electromagnetic system is used to validate the proposed parametric macromodeling technique in a practical design process flow

Partition of Unity Interpolation on Multivariate Convex Domains

In this paper we present a new algorithm for multivariate interpolation of scattered data sets lying in convex domains \Omega \subseteq \RR^N, for any $N \geq 2$. To organize the points in a multidimensional space, we build a $kd$-tree space-partitioning data structure, which is used to efficiently apply a partition of unity interpolant. This global scheme is combined with local radial basis function approximants and compactly supported weight functions. A detailed description of the algorithm for convex domains and a complexity analysis of the computational procedures are also considered. Several numerical experiments show the performances of the interpolation algorithm on various sets of Halton data points contained in $\Omega$, where $\Omega$ can be any convex domain like a 2D polygon or a 3D polyhedron

Fully parameterized macromodeling of S-parameter data by interpolation of numerator & denominator

A robust approach for parametric macromodeling of tabulated frequency responses is presented. An existing technique is modified in such a way that interpolation is performed at the numerator and denominator level, rather than the transfer function level. This enhancement ensures that the poles of the parametric macromodel are fully parameterized. It strengthens the modeling capabilities and improves the model compactness

Auto-generation of passive scalable macromodels for microwave components using scattered sequential sampling

This paper presents a method for automatic construction of stable and passive scalable macromodels for parameterized frequency responses. The method requires very little prior knowledge to build the scalable macromodels thereby considerably reducing the burden on the designers. The proposed method uses an efficient scattered sequential sampling strategy with as few expensive simulations as possible to generate accurate macromodels for the system using state-of-the-art scalable macromodeling methods. The scalable macromodels can be used as a replacement model for the actual simulator in overall design processes. Pertinent numerical results validate the proposed sequential sampling strategy

Two-dimensional interpolation using a cell-based searching procedure

In this paper we present an efficient algorithm for bivariate interpolation, which is based on the use of the partition of unity method for constructing a global interpolant. It is obtained by combining local radial basis function interpolants with locally supported weight functions. In particular, this interpolation scheme is characterized by the construction of a suitable partition of the domain in cells so that the cell structure strictly depends on the dimension of its subdomains. This fact allows us to construct an efficient cell-based searching procedure, which provides a significant reduction of CPU times. Complexity analysis and numerical results show such improvements on the algorithm performances