Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics

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    Electromagnetic Fields

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

    Last updated: 2021. március 28.

    Budapest University of Technology and Economics
    Faculty of Electrical Engineering and Informatics
    Electrical engineering, MSc
    Course ID Semester Assessment Credit Tantárgyfélév
    VIHVMA08 2 3/1/0/v 4  
    3. Course coordinator and department Dr. Pávó József,
    Web page of the course
    4. Instructors

    Dr. Gyula Veszely, professor emeritus,  BME-HVT

    Dr. József Pávó, professor, BME-HVT

    Dr. Szabolcs Gyimóthy, associate professor, BME-HVT

    Dr. Sándor Bilicz, associate professor, BME-HVT

    Dr. Árpád Bokor, honorary associate professor, BME-HVT 

    5. Required knowledge
    • Mathematics, Physics, Fundamentals of Electromagnetic Fields
    6. Pre-requisites
    NEM ( TárgyEredmény( "BMEVIHVM108" , "jegy" , _ ) >= 2
    TárgyEredmény("BMEVIHVM108", "FELVETEL", AktualisFelev()) > 0
    TárgyEredmény( "BMEVIHVMA19" , "jegy" , _ ) >= 2
    TárgyEredmény("BMEVIHVMA19", "FELVETEL", AktualisFelev()) > 0)

    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 phenomena using deductive reasoning based on the Maxwell-equations.

    In-depth discussion of the theory of electromagnetism starting from the knowledge gathered during the BSc studies.

    Understanding the basics of the various methods used for the numerical analysis of electromagnetic field problems. Discussion of relevant questions related to the modelling of electromagnetic devices. Analysis, design and optimization of electromagnetic devices in the engineering practice.

    Discussion of the electromagnetic theory behind the working principles of some devices: ranging from the high power engineering apparatuses through the high frequency applications to the optical and nanoelectronic devices.

    8. Synopsis

    I. Introduction, review of previous studies

    Week 1

    Review of the mathematics background. Maxwell-equations. Electromagnetic field quantities, forces. Constitutive relations, spatial- and time dispersion in materials. The meaning of imposed electric field. Macroscopic and microscopic Maxwell-equations and their relations. Electromagnetic field quantities at the boundary of two different materials.

    Week 2

    Energy balance, electromagnetic power density. Concept of initial value and boundary value problems. Special time dependences in linear materials: steady-state periodic excitation, arbitrary shape excitation in passive materials, causal excitations. Complex power, complex form of the energy balance.

    II. Boundary value problems in electrodynamics

    Week 3

    Conditions to get unique solution of the Maxwell-equations, the radiation condition. Boundary value problems (BVP) of electrodynamics. Scalar problems leading to the Laplace-Poisson equation: (i) electrostatics, (ii) magnetostatics, (iii) current flow problems. Boundary conditions leading to the unique solution of the Laplace-Poisson equation, the physical representation of this boundary conditions.

    Week 4

    Further BVPs of electrodynamics: (iv) magnetic field due to stationary currents defined by vector potentials or by reduced magnetic scalar potential, (v) eddy current fields (quasi-stationary fields), (vi) electromagnetic waves. Electromagnetic field representation of n-poles of Kirchhoff type networks.

    Week 5

    Demonstration (4 hours): (i) solution of electrostatic problems with finite element method (FEM) software. Definition of the BVP, derivation of the design parameters from the numerical solution of the BVP. Usage of the applied FEM software. Some further practical examples solved by FEM: magnetic field due to stationary currents, eddy current field and electromagnetic waves.

    III. Numerical solution of boundary value problems, basics of the analysis softwares used in the electrical engineering practice

    Week 6

    Review of methods used for the numerical solution of BVPs (global/local approximations, integral/differential formulations, etc.). Application of FEM for the solution of BVPs. Residuum theory, derivation of the discretized equations for Poisson-type problems. Approximating function used for FEM.

    Week 7

    Green's functions for scalar BVPs. Some 1D Green's functions. Green's functions of the scalar Poisson- and wave equations in free space. Dyadic Green's functions. Dyadic Green's functions related to the vectorial Poisson- and wave equations in free space. Method of integral equations used for the solution of the BVPs of electrodynamics.

    Week 8

    Demonstration (2 hours): examples for the solution of BVPs of electrodynamics. Finite difference time domain (FDTD) method. Discretization of the differential operator, the Yee algorithm for 1 and 3 dimensional cases. Demonstration (1 hours): analysis of multilayer anti-reflection coating for various excitations with FDTD method.

    IV. Classical electromagnetic field analysis problems in electrical engineering

    Week 9

    Time-dependent problems in lossy transmission lines, application of Fourier-transform method. Time-dependent problems in ideal transmission lines, use of the Laplace-transform method, understanding the graphical solution. Demonstration (1 hour): numerical code for the analysis of lossy transmission lines using the Fourier-transform method. Inverse and optimization methods in electrodynamics.

    Week 10

    Demonstration (2 hours): example, (i) inverse and optimization problem of electromagnetic nondestructive testing, (ii) solution of an optimization problem. High power engineering applications, eddy currents in electrical machines.

    Week 11

    Electromagnetic wave problems. Plane waves: reflection of plane waves with arbitrary incidence, total reflection, representation of arbitrary electromagnetic field as superposition of plane waves. Waveguides: eigenvalue problems, definition of modes in waveguides with arbitrary cross-sections, guided modes of waveguides with rectangular cross section. Open waveguides: microstrip waveguides, dielectric waveguides. Hertz-dipole: near- and far fields, radiation pattern, input impedance, directivity, gain. Patch antennas.

    Week 12

    Demonstration (2 hours): analysis of high frequency devices using HFSS FEM software.

    V. Selected topics from novel applications

    Electromagnetic waves in periodic structures, investigation of some meta-materials. Homogenization.

    Week 13

    Demonstration (2 hours): reflection of electromagnetic waves on periodic structures. Coupled mode theory, basics of wireless power transfer.

    Week 14

    Maxwell-equations in moving media: relativistic Maxwell-equations and its approximations. Example: scattering from moving objects.

    9. Method of instruction

    Lectures: 3 hours per week, demonstration: 1 hour per week. Demonstrations are mainly about the presentation made by the use of electromagnetic field calculation softwares. Lectures and demonstrations are not evenly distributed during the semester, they are arranged to follow the needs of the curriculum.

    10. Assessment

    a. During the lecture period: students must solve a dedicated field calculation problem. The result of this must be reported orally. The oral report will be graded, a minimum grade 2 is required for the signature.

    b. During the examination period: students must sit for an oral exam.

    c. Examination before the examination period: those who's report grade is 5 can sit for an exam during the week before the examination period.
    11. Recaps

    If the oral report is failed during the lecture period, it can be repeated once in the week before the examination period.

    12. Consultations

    Lecturers of the course offer consultation hours during the lecture period. One consultation is offered before each exam. The actual time of the consultations can be found on the web site of the course.

    13. References, textbooks and resources

    David k. Cheng, Field and wave electromagnetics, Addison-Wesley Publishing Company, Reading, MA, USA

    14. Required learning hours and assignment
    Preparation for the lectures
    Preparation for the seminars
    Preparation for the exam
    15. Syllabus prepared by

    Dr. József Pávó, professor, BME-HVT