Valentin de la Rubia

Reliable Reduced-Order Model for Fast Frequency Sweep in Microwave Circuits

AbstractIn this work, a reduced-order model for a fast and reliable frequency sweep in microwave circuits is proposed. A finite-element method approach is carried out for the circuit analysis. The ingredients of this methodology are (1) the use of field solutions at given frequencies as basis functions to reduce the original system, (2) adaptively choosing the field solution frequency samples, and (3) evaluation of the residual error of the reduced field solution to determine the convergence of the reduced-order model in the frequency band of interest. As a result, a fully automatic and reliable frequency sweep for microwave circuits is conducted.Abstract In this work, a reduced-order model for a fast and reliable frequency sweep in microwave circuits is proposed. A finite-element method approach is carried out for the circuit analysis. The ingredients of this methodology are (1) the use of field solutions at given frequencies as basis functions to reduce the original system, (2) adaptively choosing the field solution frequency samples, and (3) evaluation of the residual error of the reduced field solution to determine the convergence of the reduced-order model in the frequency band of interest. As a result, a fully automatic and reliable frequency sweep for microwave circuits is conducted.

Circuit model for microwave filters via the reduced-basis method

In this work, the electromagnetic behaviour in microwave filters is described in terms of circuit theory. A transversal coupling matrix gathering all electromagnetic phenomena within a frequency band is found. As a result, further insight from the microwave point of view arises. A Finite Element Method approach is carried out for the microwave filter analysis and a reliable reduced-order model for fast frequency sweep is proposed. The ingredients of this methodology are: 1) the use of field solutions at given frequencies as basis functions to reduce the original Maxwell system, 2) adaptively choosing the field solution frequency samples and 3) change of basis in the reduced-order model to get a transversal coupling matrix description of electromagnetics.

Geometry parametric model order reduction with randomly generated projection bases

In this work, a reduced-order model for geometry parameters and fast frequency sweep is proposed. The Finite Element Method is used to solve time-harmonic Maxwells equations. Taking into account the electromagnetic field does not arbitrarily vary as a function of frequency and geometry parameters, a low dimension system manifold is identified. Thus, the original Finite Element problem can be approximated by a model of reduced size. The basics ingredients of this approach are (1) the use of field solutions at properly selected frequencies for given geometry parameters as basis functions to project the original system, and (2) the use of a mesh deformation technique to write down the electromagnetic field upon the same mesh, i.e., preserving its topology, for different geometry parameters. This allows us to effectively take geometry parameters into account for Model-Order Reduction.

Reduced basis approximations in microwave filters and diplexers: Inf-sup constant behavior

In this work, a model order reduction technique for fast frequency sweep in microwave filters and diplexers via the Reduced Basis Method is detailed. The Finite Element Method is used to solve the time-harmonic Maxwells equations in these resonant circuit problems. Taking into account the electromagnetic field varies smoothly as a function of the frequency parameter, a low dimension system parameter manifold is identified. Thus, the original frequency-dependent Finite Element problem can be approximated by a model of reduced size using a Reduced Basis approximation. Based on the field frequency behavior in these resonant structures, the Reduced Basis space where the approximation holds is identified and characterized. Finally, special emphasis is placed in the behavior of the inf-sup constant used to provide an a posteriori error estimator, and its consequences in the Reduced Basis approximation are highlighted.

Data-driven model order reduction via Loewner approach for fast frequency sweep in hybrid BI-FEM solution in large finite frequency selective surfaces

A data-driven model order reduction technique for fast frequency sweep in computationally intensive full-wave solution in large finite frequency selective surfaces is detailed. A hybrid Boundary Integral-Finite Element Domain Decomposition Method is addressed to accurately predict the electromagnetic behavior of these structures. A reduced-order model is built up by means of output data provided by the electromagnetic solver, which is used as a black box as regards the model order reduction process. A Loewner matrix approach is taken into account to provide a tangential interpolation to S parameter output data. As a result, a dynamical system representation fitting the simulation data is obtained, and further electromagnetic insight can be earned from this system representation.

Loewner matrix approach for circuit modelling in FEM analysis of microwave filters

A circuit description of the electromagnetic behavior in microwave filters by means of the data provided by FEM analysis in the frequency band of interest is detailed. Loewner matrix approach is used to carry out a tangential interpolation of the simulation data, giving rise to a linear dynamical system description fitting the simulation results. The FEM solver is then used as a black box unlike other model-order reduction techniques. As a result, from this linear dynamical system, a transversal coupling matrix gathering all electromagnetic phenomena within a frequency band is found.