Computational Electromagnetics


Lectures for bachelor students

Electromagnetic Compatibility


Prof. L. Klinkenbusch

Target Group

"Hauptdiplom" Engineering Students


Each electrical device on the market of the European Community (and in most other countries) has to be "electromagnetically compatible", i.e., it must not disturb other devices or the environment in an inadmissible way. Moreover, such a device has to work without any trouble within an electromagnetically "contaminated" environment as well. The questions concerned with these problems are addressed by a scientific discipline, which is shortly known as "Electromagnetic Compatibility" (EMC). Although  EMC problems are as old as the technical utilization of electrical phenomena, EMC has reached a significant importance within the last decades. This is mainly a consequence of the rapid development and increasing application of electronic equipment and devices in wireless communications, which can serve as a source as well as a sensitive target of disturbing emissions. Moreover in the last years there is a public and scientific discussion about a possibly existing  influence of electrical devices on the environment (e.g. high voltage lines, mobile phones). It is clear that EMC is an interdisciplinary challenge, where different experts are involved (engineers, lawyers, physicians, biologists, politicians,...). Engineers who are familiar to EMC should be able to recognize and avoid EMC problems even in the planning stage, and to apply suitable methods while solving such problems.



Concepts and definitions, modelling, coupling mechanisms, classification of EMC problems

Shielding and Filters:

Shielding of electro- and magnetostatic fields, of low-frequency magnetic fields, and of electromagnetic waves, influence of apertures, frequency-selective filters, potential-separation and voltage limiters, cable shielding

Example: Slit-Ring Resonator

EMC Measurement Techniques:

Measuring of emitted voltages and currents, Measuring of emitted electromagnetic fields, EMC antennas, susceptibility tests for wire-bonded and for radiated interferences,

EMC of a System:

Stages of EMC considerations, modelling, systematical planning for complex systems

Electromagnetic Compatibility of the Environment:

Typical problems and examples, on public discussions on EMC.


A printed manuscript including a list of references will be distributed during the course.


For the numerical exercises computers will be provided.

Electromagnetic Fields I


Prof. L. Klinkenbusch and Staff

Target group

B.Sc. Students in Electrical Engineering


Basics of Field Theory:

Mathematical Foundations (Vector Calculus, Integral Theorems), Maxwell's Equations, Boundary Conditions


Definition, Field Equations, Scalar Potential, Poisson- and Laplace Equation,, Coulomb Integral, Image Method, Uniqueness Theorem, Capacity, Potential- and Capacity Coefficients, Dipole, Point Dipole, Polarization, Electrical Double-Layer, Energy and Forces in Electrostatics.

Stationary Fields:

Definition, Field Equations, Electric Fields of Stationary Currents (Fields in Conductors, Ohm's Law, Kirchhoff's Equations, Duality between Conductance and Capacity), Magnetic Fields of Stationary Currents (Ampere's Law, Vector Potential, Biot-Savart's Law, Magnetic Dipole, Magnetization).


... will be given during the course.

Electromagnetic Fields II


Prof. L. Klinkenbusch and Staff Members

Target group

B.Sc. Students in Electrical Engineering


Slowly-varying electric and magnetic fields:

Electric compensation processes, induction, magnetic field energy, induction coefficients, forces in magnetic fields

Electromagnetic fields and waves:

Maxwell's equations, plane waves, phase velocity, polarization, dispersion, group velocity, Poynting vector, wave guides (TEM, TE, TM), dielectric wave guide, electrodynamic potentials, Lorenz gauge, Hertzian and Fitzgerald dipoles, reciprocity theorem

Quasi-stationary fields:

Definitions, gauging, displacement-current-free quasi-stationary fields, eddy-current-free quasi stationary fields


... will be given during the course.