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 Industry, innovation and infrastructure Sustainable cities Climate Action

Academic Year 2021/2022

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. Magnetic Vector Potential, near field and far field conditions. 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. Phasors and MEs for time-harmonic regime. Complex electrical permittivity.

Continuity of the field on a plane interface. 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

- F. T. Ulaby, U. Ravaioli - Fondamenti di campi Elettromagnetici, Pearson Italia, 2021- V. Rizzoli, Lezioni di Campi Elettromagnetici, Propagazione libera e antenne, Ed. Progetto Leonardo, Bologna

For deeper insight reading:

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

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

Teaching methods

Direct lesson given by the teacher and interactive exercises. The teaching method is Inductive: from practical problems and experiments to theorization. Some parts are deductive. learning is frequently checked using interactive discussion in class.

Assessment methods

the exam consists of a written and an oral test on the entire course program. The final Mark results from the contextual evaluation of the written and oral exams. It is possible to view and possibly discuss the written test only at the oral exam. Candidates whose written test is insufficient will have to take again written and oral exam parts in a subsequent exam date. The validity of the written is limited to the current call.

In order to take  the exam, registration in Almaesami is mandatory

NOTE: For students enrolled up to A.Y. 2020-21 who have already taken the exam for module I only with the old procedure, it will be possible to take the exam for module II only within a maximum limit of 18 months from the date of module I examination.

Teaching tools

Blackboard. PC. Projector.

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

The "Insegnamenti Online" portal is used to distribute lecture notes, material and written test examples

Office hours

See the website of Vittorio Degli Esposti

See the website of Enrico Maria Vitucci