07941 - Electromagnetic Fields

Course Unit Page


This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

Affordable and clean energy Sustainable cities Climate Action

Academic Year 2018/2019

Learning outcomes

Knowledge of macroscopic electromagnetic theory in non stationary conditions. Knowledge of basic electromagnetic propagation phenomena in sourceless, free space cases and in presence of sources: plane wave and spherical wave propagation. Basic knowlenge of emission, transmission and reception of radio signals. At the end of the course the student is able to master the basic design of single-link radio transmission systems, including simple propagation impairments such as surface reflection.The student knows the basic antenna parameters for both single-element and multi-element antennas. Transmission lines and waveguides. The scattering matrix. Applications to front ends and RF circuits.

Course contents

--------- Part I ----------

Recall of Maxwell Equations (ME) in integral and differential form. Sources and sinks.

Continuity of the field on a plane interface. Phasors and MEs. Complex electrical permittivity.

Energy relations: Poynting's theorem and vector. The uniqueness theorem of the solution.

Maxwell’s problem in absence of sources: a solution of the MEs in a mono-dimensional domain: wave equations in time and frequency domains. The general solution of the Helmholtz equation: plane TEM waves. Reflection and refraction of plane waves. Guided propagation principles: total reflection, principle of optical fibers. Polarization.

Maxwell’s problem in presence of sources. Solution of MEs using the vector potential.

The field generated by an infinitesimal current element. Near and far field conditions. spherical waves and local plane waves.

Finite sources: radiation vector, far field condition vs. the wavelength and size of the source.

Antennas characterization, radiation function, radiation pattern. Characterization of an antenna in emission and reception. Effective area, efficiency, directivity and gain. Most common antennas. Transmission formula and applications. Radio link budget.

Short dipoles and arrays of dipoles.

---------- Part II ----------

General principles of guided wave propagation. The concept of propagation mode and classification of modes: TEM, TE and TM. Hybrid modes (outline). Quasi-TEM modes

Equivalent circuit description of TEM and quasi-TEM propagation: transmission lines.

Electromagnetic concept of an electric network and its applications: the scattering matrix.

Complex conjugate and impedance matching. Impedance matching devices: use of Smith's chart.

Planar Circuit technology. Design of microstrip and stripline structures. Design of transmission media: coaxial cable, wire lines and rectangular waveguides.


- Duplicated lecture notes

- G. Conciauro - Introduzione alle onde elettromagnetiche, Mc. Graw Hill (english version available)

- V. Rizzoli, Lezioni di Campi Elettromagnetici, Propagazione libera e antenne, Ed. Progetto Leonardo, Bologna

- P. Bassi et alii, "Introduzione ai campi elettromagnetici", Bononia University Press, 2016

-V. Rizzoli, A. Lipparini, "Propagazione elettromagnetica guidata" Esculapio, Bologna, 1998

Teaching methods

The teaching method is Inductive: from practical problems and experiments to theorization. Some parts are deductive

Assessment methods

For Part I the exam consists of an a written test and of an oral test. The final mark is the overall evaluation of both written and oral tests. It is possible to vision and discuss the written test manuscript only during the oral test. If written test average mark is insufficient (below 18 out of 30) the candidate must skip the oral exam and take the whole exam again on a successive exam date.

For part II the exam consists of a written problem with possible oral integration at the discretion of the teacher.

NOTE: The final mark of the exam for “Electromagnetic Fields”, first module, is saved in the archive until the date of the exam for the second module:  after that, the weighted average mark is recorded in the student’s electronic record. The examination of the second module will have to be taken within 18 months from the first module exam: after that the candidate will have to take again the exam for the first part. The exam for the I module must be taken BEFORE the exam for the II module

Teaching tools

Blackboard. PC. Projector.

Didactic antenna set including generator, sample antennas, receiver and tools

Office hours

See the website of Vittorio Degli Esposti

See the website of Enrico Maria Vitucci