Applied Electromagnetics

Course Description

The curse deals with the basic phenomena associated with time-varying electromagnetic fields. The radiation and propagation of the electromagnetic waves in unbounded media and along the guiding structures are analyzed mathematically together with clear physical interpretation. The experimental demonstration of all analyzed phenomena with examples of practical applications in various engineering systems such as communications, electronics and computers are given.

General Competencies

Clear and deep understanding the basic physical phenomena associated with radiation and propagation of the electromagnetic waves together with appropriate mathematical analysis. After completed course the students are expected to be able to understand basic principles of various engineering systems that make use of time-varying electromagnetic fields (wireless communication systems, optical communication systems, radio frequency and microwave electronic systems, high-speed digital systems). It is also expected that students will develop the competence to solve a broad range of practical problems in these systems.

Learning Outcomes

  1. Explain physical background of propagation of EM waves in free space, in unbounded loss-free and lossy dielectric as well as the propagation along guiding structures
  2. Explain physical background of Maxwell equations in integral and differential forms, vector wave equation and associated solutions for travelling wave, standing wave and evanescent wave
  3. Explain physical background of radiation of EM wave, elemental electric dipole and a simple antenna array with two radiators
  4. Calculate basic parameters (a characteristic impedance and propagation constant) of simple guiding structures: TEM transmission line, dielectric slab and rectangular waveguide
  5. Calculate all the parameters needed for matching of an arbitrary load to the generator using one-stub matching circuit
  6. Calculate the EM field distribution in the case of propagation of EM wave that impinge onto dielectric half-space or multi-layer dielectric from the free space, at normal and oblique incidence
  7. Identify components for radiation and propagation of EM waves in practical engineering systems in communications in electronics and explain associated background physics

Forms of Teaching


Theoretical background of each unit is given in the lectures. This is complemented by in-front-of-class experiments and computer situations that explain physics of particular phenomenon.


Short conceptual problems and numerical problems.


Numerical examples of realistic engineering electromagentic problems are solved in details.

Laboratory Work

Three blocks of laboratory exercises. Each exercise is run as a group work of four students.


There are 10 in-front-of-class experiments that cover whole syllabus. Each experiment is recorded by camera and projected on the screen. Therefore, each student is able to follow the experiment. Each experiment is also complemented by computer simulation, which enables further discussion and analysis.


There are weekly scheduled consultations with a professor and a teaching assistant. For some special problems, the group consultations are also organized occasionally

Grading Method

Continuous Assessment Exam
Type Threshold Percent of Grade Threshold Percent of Grade
Laboratory Exercises 0 % 10 % 0 % 10 %
Homeworks 0 % 5 % 0 % 5 %
Quizzes 0 % 3 % 0 % 3 %
Class participation 0 % 3 % 0 % 3 %
Attendance 0 % 1 % 0 % 1 %
Mid Term Exam: Written 0 % 10 % 0 %
Final Exam: Written 0 % 18 %
Final Exam: Oral 50 %
Exam: Written 0 % 28 %
Exam: Oral 50 %

Week by Week Schedule

  1. Introduction – The importance of electromagnetics in engineering. Brief review of applications of time-varying electromagnetic fields in different engineering systems such as communications, electronics and computers. Distributed parameters, general transmission line equation and its solutions.
  2. Distributed parameters, general transmission line equation and its solutions. Physical interpretation of transmission line equations: reflection, a standing wave, matching. Analogy between propagation of the electromagnetic wave along a transmission line and propagation in homogenous dielectric.
  3. Smith chart. Practical problem of matching of an antenna to transmitter or a receiver. Laboratory exercises - Part I - Propagation of EM waves along TEM transmission line and matching
  4. Maxwell equations, wave equation. The basic solutions of vector wave equation. Physical interpretation of the solutions: traveling plane wave, an evanescent wave, a standing wave.
  5. Group velocity, flux of electromagnetic energy, Poynting vector. Plane wave propagation in infinite homogenous media. Lossless and lossy case.
  6. Normal incidence of a plane wave on a homogenous dielectric half space including multilayer problem. Lossless and lossy case.
  7. Oblique incidence of a plane wave on a homogenous dielectric half space including multilayer problem. Lossless and lossy case. Laboratory exercises - Part II - Basic properties of EM wave in free-space
  8. Midterm exam
  9. Propagation of electromagnetic wave along a general uniform guiding structure. Parallel-plate waveguide
  10. Rectangular waveguide, TE and TM modes of propagation.
  11. Circular waveguide, electromagnetic resonators.
  12. Propagation in dielectric slab, dielectric waveguide.
  13. Introduction to radiation, magnetic vector potential, elemental Hertz dipole
  14. Basic antenna parameters, radiation pattern, radiation resistance, directivity and gain. A simple linear (wire) antenna. The concept of antenna array. A simple antenna array comprising two radiators. Laboratory exercises Part III- Waveguides and radiation of EM waves
  15. Final exam

Study Programmes

University undergraduate
[FER2-HR] Electronics - module
Specialization courses (5. semester)
[FER2-HR] Wireless Technologies - module
(5. semester)


Z. Smrkić (1986.), Mikrovalna elektronika, Školska Knjiga
Staelin, Morgenthaler, Kong (1994.), Electromagnetic Waves, Prentice Hall
C.Balanis (1989.), Advanced Engineering Electromagnetics, John Willey
F. Ulaby (.), Fundamentals of Applied Electromagentics,


Laboratory exercises

For students


ID 86507
  Winter semester
L2 English Level
L1 e-Learning
45 Lectures
0 Seminar
9 Exercises
15 Laboratory exercises
0 Project laboratory

Grading System

90 Excellent
80 Very Good
60 Good
50 Sufficient