vissza a tantárgylistához   nyomtatható verzió    

    Computational Electromagnetics

    A tantárgy neve magyarul / Name of the subject in Hungarian: Elektromágneses terek modellezése

    Last updated: 2024. október 22.

    Budapest University of Technology and Economics
    Faculty of Electrical Engineering and Informatics     		Computational Electromagnetics
    Course ID Semester Assessment Credit Tantárgyfélév
    VIHVA002   2/0/2/v 4  
    3. Course coordinator and department Dr. Pávó József,
    4. Instructors

    József Pavó, professor, HVT

    Sándor Bilicz, associate professor, HVT

    Szabolcs Gyimóthy, professor, HVT

    5. Required knowledge Matematika A1a
    Matematika A2a
    Villamosságtan mechatronikai mérnököknek (BMEVIAUA035)

    6. Pre-requisites
    Kötelező:
    TárgyTeljesítve("BMETE9_BG02") VAGY
    (TárgyTeljesítve("BMETE93BG20") ÉS
    TárgyTeljesítve("BMETE93BG22"))

    A fenti forma a Neptun sajátja, ezen technikai okokból nem változtattunk.

    A kötelező előtanulmányi rend az adott szak honlapján és képzési programjában található.

    7. Objectives, learning outcomes and obtained knowledge - The main goal of the course is the qualitative and quantitative discussion of the electromagnetic (EM) phenomena using deductive reasoning based on the Maxwell-equations.

    - Understanding the basics of the various methods used for the numerical analysis of EM field problems. Discussion of relevant questions related to the modeling and design of EM devices.

    - Application of the finite element method (FEM) for EM field modeling, discussion of the boundary value problems associated to various EM field problems.

    - Discussion of the electromagnetic theory behind the working principles of some devices being relevant in the mechatronics engineering practice.
    8. Synopsis
    Week 1:
    Introduction. Discussion on the personal projects, on the homework and on the examination. Scope of the lectures. Maxwell-equations, constitutive relations, differential Ohm’s law, understanding and demonstrating the impressed electric field and current density. Continuity of field quantities at the interface of two materials. Macroscopic and microscopic Maxwell-equations. Classification of the material properties: linear and nonlinear; isotropic, anisotropic and bi-anisotropic; time- or spatial dispersion, etc. Mathematical backgrounds: vector fields, reviewing the basics used from vector algebra.

    Week 2:
    Orthogonal co-ordinate systems (Descartes, Cylindrical, Spherical). Derivatives in general orthogonal co-ordinate systems. Energy balance, electromagnetic power density. Conditions to get unique solution of the Maxwell-equations: proof of the theorem. The radiation condition for unbounded domain. Concept of initial value and boundary value problems. Classification of the practical problems of electrodynamics. Time independent problems: (i) Electrostatics, (ii) Current flow fields, (iii) Magnetostatics, (iv) Magnetic field of steady currents.

    Week 3:
    Classification of the practical problems of electrodynamics (continuation): Time dependent fields: (v) Quasistatic problems: Magneto-quasistatic (eddy current), Electro-quasistatic and Electromagneto-quasistatic problems, (vi) Electromagnetic waves. The boundary value problem (BVP) of electrostatics. Introduction of the scalar potential. Physical meaning of the boundary conditions. Capacitance, partial capacitance. Proof of the unicity of the solution of the BVP of electrostatics. Short review of selected problems of electrostatics having analytical solutions.

    Week 4:
    Electrostatic energy of the field due to charged conductors. 2D field problems in general. Solution of an electrostatic problem with PDE Toolbox of Matlab. Introduction to the use of the software: input of the geometry, setting up the BVP, postprocessing the results.

    Week 5:
    Week formulation of the BVP related to the Laplace-Poisson's equation. Some words about the FEM developed for the solution of problems leading to the BVP of Laplace-Poisson's equation. 1D numerical example for FEM discretization based on the weak formulation. BVP of stationary conduction (current flow) fields. Review of selected problems of stationary conduction having analytical solutions.

    Week 6:
    Demonstration: solution of two current flow field problems with PDE Toolbox of Matlab. Introduction to the use of the software for problems with cylindrical symmetry, some notes on coupled problem of current flow field and electrostatics.

    Week 7:
    BVP of magnetostatics. Demonstration: solution of a magnetostatic field problem with PDE Toolbox of Matlab: analysis of Deprez-type multimeter. Introduction to the analysis of configurations containing permanent magnets (ferromagnetic materials with nonlinear magnetization).

    Week 8:
    Magnetic fields of stationary currents: the governing equations and the BVP based on magnetic vector potential, A. The BVP and its solution for free space, the Biot-Savart law. Review of selected problems of magnetic fields of stationary currents having analytical solutions. Formulation of the BVP in 2D situations: planar 2D problems and configurations with cylindrical symmetry, description of the related BVPs with one component vector potential. Demonstration of the solution of 2D magnetic field problems of stationary currents: analysis of the force of a cylindrical shape magnetic actuator and the inductances of a cylindrical transformer.

    Week 9:
    Time-dependent electromagnetic fields: introduction, consequences of the time dependence. Steady-state sinusoidal excitation, the complex calculation method: introduction of the method trough a 1D example from vibration theory. Special time dependences: constant excitation, steady-state sinusoidal periodic excitation. The complex calculation method representation of vector fields with complex vectors. Complex power, complex form of the energy balance. Steady-state periodic excitation in linear materials: solution by using the complex calculation method and Fourier-series. Excitation with arbitrary time dependence in linear passive materials: application of Fourier-transform. Consideration of causal excitation (Laplace-transform).

    Week 10:
    Time dependent electromagnetic fields. Quasistationary fields: Magneto-, electro- and electromagneto-quasistationary fields. Eddy-current (magneto-quasistationary) fields. Analytical expression of eddy-currents in conducting half-space. Review of selected problems of magnetic induction and eddy current fields having analytical solutions.

    Week 11:
    BVP of the magneto-quasistationary fields (eddy-current fields), the BVP in 2D. Demonstration of the solution of an eddy-current problem in cylindrical symmetry: analysis of induction cooker, discussion on the impedance type boundary condition.

    Week 12:
    Elektromagnetic waves. Introduction of the topic, typical sets of problems related to EM waves: (i) generation of EM waves, (ii) propagation and scattering of EM waves and (iii) guided waves. Electromagnetic field of a Hertzian dipole. Characterization of antennas. Some typical antenna types. Demonstration of the calculation of the radiated EM waves of a dipole antenna.

    Week 13:
    Typical boundary conditions related to EM wave problems, the BVP of EM waves, the eigenvalue problems, the guided modes of rectangular waveguides. Propagation and scattering of EM waves: theory and demonsrations. Plane waves. Transmission lines.

    Week 14:
    Review of the studies of the semester.

    9. Method of instruction Lectures (2 hours/week) and laboratory demonstrations (2 hours/week), both are presented for the whole group of students in the same time.
    10. Assessment The homework in a form of a project task will assigned to each student individually between the 8-10th week of the semester. The project involves solving a complex field calculation problem.

    Signature:
    Student must present a plan for the solution of his/her project during a personal consultation with the lecturer. The signature is granted if the orientation of student is proved to be sufficient for the completion of the project during the examination period.

    Examination:
    For the examination students complete their projects: prepare the calculation model, perform the calculations, complete the design task and comment the results, etc. The process of solving the problem and the results must be documented in writing, and the solution must also be presented in an oral report based on the written documentation. The documentation must be submitted by 12:00 noon the day before the examination. The oral presentation takes place during the examination, all students taking the examination on a given day are present and listen to each-others report. The audience may put any questions related the presentation and at the end the instructor will evaluate both the documentation and the oral presentation with an examination evaluation ranging from fail (1) to excellent (5).
    11. Recaps Those who do not get signature during the term time, may try to get it during the week before the examination period.
    12. Consultations Each student has the opportunity to have an individual consultation with the lecturer or an instructor designated by the lecturer, as many times as needed. Consultations can take place during the periods designated by the instructors, which are arranged in such a way that everyone has the chance to attend the desired number of consultations. Typically, at least one consultation is required during the term time, and 2-3 consultations during the exam period.
    13. References, textbooks and resources 1. Online materials provided by the lecturer via the educational portal

    2. P.P Silvester, R.L. Ferrari, Finite Elements for Electrical Engineers, 3ed, Cambridge University Press, 2008

    3. Jian-Ming Jin, The Finite Element Method in Electromagnetics, 3ed, Wiley-IEEE Press, 2014

    4. Simonyi Károly, Zombory László, Elméleti villamosságtan, 12. átdolgozott kiadás, Műszaki Köszvkiadó, Budapest, 2000.

    5. David J. Griffiths, Introduction to Electrodynamics, 4ed, Pearson Education Limited, 2014

    14. Required learning hours and assignment
    Kontakt óra 56
    Félévközi készülés órákra 6
    Felkészülés zárthelyire 0
    Házi feladat elkészítése 10
    Kijelölt írásos tananyag elsajátítása 8
    Vizsgafelkészülés 40
    Összesen 120
    15. Syllabus prepared by József Pavó, professor, HVT