SUMMARYThis paper presents two sequential sampling algorithms for the macromodeling of parameterized system responses in model-dependent sampling frameworks. The construction of efficient algorithms for the automatic selection of samples for building scalable macromodels of frequency-domain responses is addressed in this paper. The sequential sampling algorithms proposed here are tailored towards the application of local scalable macromodeling schemes on unstructured design space grids. Two pertinent examples are considered. For the first one, different algorithms are applied and a comparison is made in terms of the number of samples generated, accuracy and CPU time. As a second example, four design variables are taken into account with one of the proposed algorithms and the generated model is used in a frequency-domain optimization.
This letter presents an enhanced parametric macromodeling scheme for linear high-frequency systems based on the use of multiple frequency scaling coefficients and a sequential sampling algorithm to fully automate the entire modeling process. The proposed method is applied on a ring resonator bandpass filter example and compared with another state-ofthe-art macromodeling method to show its improved modeling capability and reduced setup time.Introduction: Design activities of electromagnetic (EM) systems such as design space exploration, optimization, sensitivity analysis, etc., often require a substantial number of computationally expensive EM simulations. The development of parametric macromodels acting as accurate and efficient surrogate models for complex EM systems is an active field of research [1,2, 3, 4]. These models tend to be good approximations of the EM system behavior, characterized by frequency and additional design parameters (such as geometrical or substrate features) and can be used to speed-up the design process. Robust interpolation-based parametric macromodeling methods have been proposed over the recent years, based on the parameterization of a set of frequency-dependent rational models called root macromodels [1], [4]. In [4], interpolation of root macromodels at the input-output level, based on two scaling coefficients was presented : one of the coefficients is a multiplicative factor at the input/output level of the system (amplitude scaling) and the other coefficient is a compression or expansion term for the Laplace variable s (frequency scaling). The approach of [4] results in high modeling capability and robustness.In this letter, the parametric macromodeling method proposed in [4] is generalized by using multiple frequency scaling coefficients for all partial fractions of the root macromodels. This allows to model the behavior of the partial fractions of the root macromodels independently, in order to achieve a more flexible modeling capability. The proposed method is compared with the approach described in [4] to show its enhanced modeling capability and reduced CPU setup time.
SUMMARYA new method for gradient-based optimization of electromagnetic systems using parametric sensitivity macromodels is presented. Parametric macromodels accurately describe the parameterized frequency behavior of electromagnetic systems and their corresponding parameterized sensitivity responses with respect to design parameters, such as layout and substrate parameters. A set of frequency-dependent rational models is built at a set of design space points by using the vector fitting method and converted into a state-space form. Then, this set of state-space matrices is parameterized with a proper choice of interpolation schemes, such that parametric sensitivity macromodels can be computed. These parametric macromodels, along with the corresponding parametric sensitivity macromodels, can be used in a gradient-based design optimization process. The importance of parameterized sensitivity information for an efficient and accurate design optimization is shown in the two numerical microwave examples.
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