# Engineering Electromagnetics

## Overall Course Objectives

The course aims to introduce electromagnetics so that the basic laws, which in the course are applied to idealised special cases, can be used to estimate the behaviour of realistic electrical systems. In addition to classical electromagnetism, the students should be able to make simple calculations on important transmission line circuits, e.g. for high-speed digital electronics or microwave engineering. Additionally, the students should be trained in combining theoretical considerations with quantitative calculations from computer programs such as Matlab and laboratory measurements generated using standard instruments such as e.g. oscilloscopes, signal generators and network analysers. Finally, the course is the first one in a sequence of courses intended for students pursuing a carrier in antenna- or microwave circuit design.

**Learning Objectives**

**Learning Objectives**

- describe waves and wave propagation mathematically in the time and frequency domain using phasors and be able to translate between the two representations.
- calculate propagation and attenuation in transmission lines based on physical parameters such as dimensions and dielectric properties.
- calculate voltages, currents, transmitted power, etc. in cascaded transmission line circuits for time-harmonic signals.
- give a mathematical description of plane waves in homogeneous media and explain the concept of polarization.
- calculate reflection and transmission coefficients for plane waves for normal and oblique incidence at plane interfaces between dielectrics. Explain parallel and perpendicular polarization and choose corresponding Fresnel reflection coefficients.
- explain common antenna parameters, e.g. radiation diagram, gain, and directivity. Calculate the input impedance of basic antennas, e.g. Hertzian Dipole, half-wavelength dipole.
- explain Friis’s transmission formula and calculate the link-budget of basic communication systems.
- explain the electrostatic field quantities and the constitutive parameters. Explain Coulomb’s law, Gauss’ law and the concepts of potential, capacitance, and polarization.
- use knowledge of the behaviour of the electric field in conductors and dielectrics together with the boundary conditions for calculation of the capacitance of idealized special geometries.
- explain the magnetostatic field quantities and the constitutive parameters. Explain Biot-Savart’s law, Gauss’ law for magnetism and the concept of inductance.
- use the knowledge of the behaviour of the magnetic field around conductors together with the boundary conditions for calculation of the inductance of idealized special geometries.
- use mathematical software e.g. Matlab in support of calculations. Apply Danish as well as English electro-technical terminology.

**Course Content**

**Course Content**

– Maxwell’s equations.

– Waves and phasors, frequency, wave number, attenuation constant, propagation constant.

– Transmission lines, transmission line parameters (R’, L’, G’, C’), telegraphers equations, characteristic impedance, reflection and transmission coefficients, standing wave ratio, input impedance, power flow, Smith chart, impedance matching, quarter-wave transformer, single-stub tuner.

– Coaxial cable, two-wire transmission line, microstrip transmission line.

– Plane waves, intrinsic impedance, propagation constant, linear, circular, and elliptical polarization, parallel and perpendicular polarization, Fresnel reflection coefficients, Brewster angle, Poynting vector and power flow.

– Radiation and Antennas: radiation diagram, gain, directivity, input impedance, Hertzian dipole, half-wavelength dipole, Friis’s transmission formula, link-budget

– Vector analysis, gradient, divergence, curl, cylindrical coordinates, spherical coordinates.

– Electrostatics, electric field quantities, charge and charge density, dielectric constant, Coulomb’s law, Gauss’ law, (electric) potential, perfect conductor, conductor with losses, isolators (dielectrics), polarization, boundary conditions, capacitance.

– Magnetostatics, magnetic field quantities, the Biot-Savart law, Gauss law for magnetostatics, magnetic materials and permeability, boundary conditions.

– Induction, Faraday’s law, Lenz’ law, self-inductance, mutual inductance.

– Matlab.

**Teaching Method**

**Teaching Method**

Class lectures, group tutorials, and home assignments

**Faculty**

**Faculty**

## Michael Mattes

## Rasmus Elkjær Jacobsen

**Remarks**

**Remarks**

For students beginning in February, the course is recommended in the 4th (and not in the 3rd) semester. The learning objective for applying Danish as well as English electro-technical terminology is due to the central position of the course in the Electrical Engineering education. Danish-speaking students must acquire the Danish as well as the English electro-technical terminology, while the non-Danish speaking students must acquire the English electro-technical terminology.

E-learning is used in the form of online quizzes (home assignments), web-based tools and digital exam.