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

• Sándor BILICZ, associate professor
• Árpád BOKOR, honorary associate professor
• Szabolcs GYIMÓTHY, full professor
• József PÁVÓ, full professor

Mathematics: linear algebra, vector calculus, complex algebra, differential equations

Physics: basics of electrodynamics

Signals and systems: circuit theory, lumped and distributed parameter models, two-ports, frequency domain analysis

The course teaches the fundamentals of classical electrodynamics in an engineering approach. The main goals include

• to introduce the most important electrical engineering concepts and relationships related to classical electrodynamics,
• to present the mathematical approach related to the main applications of electrical engineering,
• to introduce the student to the way of modelling and the application of some analytical and numerical computational methods,
• to point out the relationship between the applied lumped parameter and continuum models.

a) Lectures

Summary of the fundamentals of electrodynamics, as known from preliminary studies (2 lectures): Source quantities (charge/current density), charge conservation. Vector fields (electric/magnetic field strength, displacement, magnetic flux density) and integral quantities (EMF, MMF, electric/magnetic flux). Lorentz force. Macroscopic effects of electromagnetic fields in medium (polarization, magnetization), material characteristics (permittivity, permeability, specific conductivity). Maxwell's equations in differential and integral form. Continuity of EM fields on material interfaces. Poynting's theorem of energy conservation.

Typical problems of applied electromagnetics, a classification (1 lecture)

Electrostatics (2 lectures): Scalar potential and Laplace-Poisson equation of electrostatics, solution for homogeneous medium. Boundary value problem. Charge substitution, the method of images. Electrodes, capacitance, grounding.

Static current flow (1 lecture): Laplace equation, analogies with electrostatics. The concept of resistance and its generalization for electrode system.

Static magnetic field and induction phenomena (1 lecture): Vector potential and the vectorial Laplace-Poisson equation. Biot-Savart law. Concept of self and mutual inductance. Induction law, transformer/motional EMF.

Wave propagation (2 lectures): Phasor representation of vector fields, wave equation for E or H, Helmholtz equation and its plane wave solution. Analogy with transmission lines. Plane waves in dielectric material, polarization, reflection and refraction. Plane waves in good conductors, eddy current phenomena.

Transmission and reception of waves (2 lectures): Inhomogeneous wave equation for the potentials. Field of a Hertzian dipole. Concept of near/far field. Antenna characteristics (demonstrated on the Hertzian dipole).

Waveguides (2 lectures): TEM/TE/TM propagation, eigenvalue problem, concept of modes, dispersion equation, cutoff frequency (demonstrated on the rectangular waveguide). S-parameters.

b) Classroom practices

• Revisiting the necessary mathematical tools (1 exercise)
• Solving simple but relevant analytical calculus problems on the topics covered in the lecture (6 exercises)
• Application of the finite element method to solve boundary value problems; user-level introduction to the Matlab PDE Toolbox (1 exercise)
• Numerical solution of simple two- and three-dimensional field computational problems in the topics covered in the lecture (5 exercises). This will include typical problems in electrostatics, steady currents, magnetic field, eddy currents, wave propagation and scattering.

Exercises using analytical and numerical calculations will be selected according to the current material in the lectures. The exercises will focus on the construction of a practically simplified, i.e. "tractable" mathematical model of the problem and, where relevant, on the mapping of the field computation model to a circuit model and the definition of its parameters. For the numerical calculations, the Matlab PDE Toolbox is generally used; in addition to being able to follow the calculations on a projector, the student can reproduce them on his/her laptop.

1. During the semester, two tests are written and graded 1-5. In order to obtain a signature, the two tests must have an average score of 2.0 as a minimum, but there is no minimum requirement for each of them. (An unsigned test will be counted as a 1 for the purpose of averaging.)
2. The examination is oral, based on a paper-based test, preceded by a written or oral test.
3. Pre-exam: not available

• K. Simonyi, Foundations of Electrical Engineering, Pergamon, 1963.
• D.K. Cheng, Field and Wave Electromagnetics, Addison-Wesley, 1989.
• L. Solymar, Lectures on Electromagnetic Theory: A Short Course for Engineers, Oxford University Press, 1976.
• J.D. Jackson, Classical Electrodynamics, Wiley, 1999.

• Sándor BILICZ, associate professor
• Szabolcs GYIMÓTHY, full professor
• József PÁVÓ, full professor