Gergely Koczka

Optimal Convergence of the Fixed-Point Method for Nonlinear Eddy Current Problems

A method is presented for the optimal choice of the fixed-point reluctivity in nonlinear eddy current problems solved for steady-state in the frequency and the time domain. The optimal selection is shown to ensure a minimal contraction number for the fixed-point method. The proposed technique is compared to earlier approaches using a 2-D example.

Fast Time-Domain Finite Element Analysis of 3-D Nonlinear Time-Periodic Eddy Current Problems With

A method is presented for obtaining the steady-state solution of three-dimensional eddy current problems with nonlinear material properties and periodic excitations using the T, Φ-Φ formulation. The problem is formulated in the time-domain and the application of a fixed-point approach combined with a discrete Fourier-transformation technique ensures that, during one nonlinear iteration step, there is no coupling between the time-steps within one period. The steady-state result is hence obtained by solving half as many time steps as their number in one period. Since the time steps are decoupled, their computation can be readily parallelized resulting in a fast method. Comparison with results obtained by a transient time-stepping technique is presented.

{\rm T},\Phi-\Phi

A finite element method for the analysis of three-phase, three-limb power transformers under dc bias is presented. The phase voltages and the dc components of the phase currents are assumed to be given. Using parallel algorithms, the steady-state periodic solution is obtained without stepping through the transients using a fixed-point method to solve the nonlinear equations. A novel technique to obtain the starting solution for the fixed-point iterations to ensure fast convergence is introduced. The solution to a large, real world problem is presented.

Formulation

In ultra-high-frequency radio-frequency-identification (UHF-RFID) the conjugate complex matching of the packaged UHF-RFID transponder IC and the tag antenna structure is important to increase the reading range of the transponder tag. Quite often half-wavelength dipole-like antenna structures are used. Due to the fact that the impedances of the packaged IC and the dipole antenna structure are in different domains, a matching structure is needed to accomplish the conjugate complex matching. A common technique to carry out the matching is the so called T-match. Since the nominal input impedance of the IC depends on the applied antenna voltage (and in a strongly non-linear way), the backscatter abilities of the tag are also functions of the applied voltage. In the present work those dependencies are investigated in terms of full-wave finite element simulations and measurements.

Finite Element Analysis of Three-Phase Three-Limb Power Transformers Under DC Bias

In radio frequency identification (RFID), the design and investigation of ultra-high-frequency (UHF) circular loop antennas used as reader antennas as well as tag antennas is of growing importance. Since these antennas are electrically short, a 2-D finite-element method (FEM) analysis using a single-component magnetic vector potential together with perfectly matched layers (PMLs) at the boundary is proposed in this paper in order to perform very fast and accurate axisymmetric simulations compared to very time-consuming 3-D calculations. In addition, the capacitances of the tag loops have been calculated using a 3-D quasi-static electric approach taking the gap of the loops into account.

Influence of the Non-Linear UHF-RFID IC Impedance on the Backscatter Abilities of a T-Match Tag Antenna Design

Purpose – The purpose of the paper is to show the application of the fixed‐point method with the T, Φ‐Φ formulation to get the steady‐state solution of the quasi‐static Maxwells equations with non‐linear material properties and periodic excitations.Design/methodology/approach – The fixed‐point method is used to solve the problem arising from the non‐linear material properties. The harmonic balance principle and a time periodic technique give the periodic solution in all non‐linear iterations. The optimal parameter of the fixed‐point method is investigated to accelerate its convergence speed.Findings – The Galerkin equations of the DC part are found to be different from those of the higher harmonics. The optimal parameter of the fixed‐point method is determined.Originality/value – The establishment of the Galerkin equations of the DC part is a new result. The method is first used to solve three‐dimensional problems with the T, Φ‐Φ formulation.

Investigation of UHF Circular Loop Antennas for RFID

Purpose – The purpose of the paper is to present a method for efficiently obtaining the steady‐state solution of the quasi‐static Maxwells equations in case of nonlinear material properties and periodic excitations.Design/methodology/approach – The fixed‐point method is used to take account of the nonlinearity of the material properties. The harmonic balance principle and a time periodic technique give the periodic solution in all nonlinear iterations. Owing to the application of the fixed‐point technique the harmonics are decoupled. The optimal parameter of the fixed‐point method is determined to accelerate its convergence speed. It is shown how this algorithm works with iterative linear equation solvers.Findings – The optimal parameter of the fixed‐point method is determined and it is also shown how this method works if the equation systems are solved iteratively.Originality/value – The convergence criterion of the iterative linear equation solver is determined. The method is used to solve three‐dimens...

Fixed‐point method for solving non linear periodic eddy current problems with T, Φ‐Φ formulation

Purpose A transformer model is used as a benchmark for testing various methods to solve 3D nonlinear periodic eddy current problems. This paper aims to set up a nonlinear magnetic circuit problem to assess the solving procedure of the nonlinear equation system for determining the influence of various special techniques on the convergence of nonlinear iterations and hence the computational time. Design/methodology/approach Using the T,ϕ-ϕ formulation and the harmonic balance fixed-point approach, two techniques are investigated: the so-called “separate method” and the “combined method” for solving the equation system. When using the finite element method (FEM), the elapsed time for solving a problem is dominated by the conjugate gradient (CG) iteration process. The motivation for treating the equations of the voltage excitations separately from the rest of the equation system is to achieve a better-conditioned matrix system to determine the field quantities and hence a faster convergence of the CG process. Findings In fact, both methods are suitable for nonlinear computation, and for comparing the final results, the methods are equally good. Applying the combined method, the number of iterations to be executed to achieve a meaningful result is considerably less than using the separated method. Originality/value To facilitate a quick analysis, a simplified magnetic circuit model of the 3D problem was generated to assess how the different ways of solutions will affect the full 3D solving process. This investigation of a simple magnetic circuit problem to evaluate the benefits of computational methods provides the basis for considering this formulation in a 3D-FEM code for further investigation.

Optimal fixed‐point method for solving 3D nonlinear periodic eddy current problems

Two algorithms for the implementation of fixed-point techniques applied to the solution of three-dimensional nonlinear periodic eddy current problems with voltage excited coils are compared with respect to their convergence properties. The difference is in the treatment of the equations of the voltage constraint during the fixed-point iterations. The investigations are carried out on a transformer model.

A nonlinear magnetic circuit model for periodic eddy current problems using T,ϕ-ϕ formulation

Abstract Solving electromagnetic wave propagation problems with the finite-element method results in a large number of unknowns due to the necessity of modeling an extensive portion of the surroundings of the conducting structures. These equation systems are often ill-conditioned because of the great material differences as well as changes in size between neighboring elements. In addition, the resulting matrices are indefinite. Common iterative methods exhibit poor convergence due to these conditions. Direct solution techniques result in high memory requirements. The aim of this article is to present an approach with smaller memory demand than the direct methods and better convergence properties than common iterative techniques. An iterative method based on domain decomposition is presented and compared to various conventional iterative and direct solution techniques.