Electromagnetic Fields

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.