Teaching activities

Students can find here some information on the the academic courses I am involved in, spanning from their contents to additional teaching material (books, exams and solutions...).

For any question relative to the courses, please send me an email, ring me or knock on my office door.


Objectives of the course

The EMSP course is aimed at providing students with an introductory, yet solid, knowledge of the physics of ElectroMagnetic (EM) waves and basic Signal Processing (SP) methods, specifically intended for future space engineers interested in approaching the application side of the Spaceborne Industry. The EMSP course concerns methodological aspects, intended to complement and enrich the students' background by providing the necessary knowledge not to get lost in space when it comes to handling some kind of information.

Contents (first part of the course)

The topics of the course are (first part):

  • Electrostatic field: electric charge, Coulomb’s force, main properties of the field. Interaction of materials with electric field: conductors and dielectrics
  • Magnetostatic field: Current and current density. Main properties of the magnetostatic field. Magnetic polarization
  • Time variant fields and plane waves: Maxwell’s’ equations and EM fields. Wave equation and its solution for plane waves in the time-space and phasorial domains. Propagation velocity, propagation constant. Lossless and lossy media. Reflection and refraction of EM waves due to discontinuities in the media: orthogonal (TEM) and slant (TE and TM)
  • Antennas: basic parameters of antennas (directivity, gain, directivity function, efficiency, beamwidth, …), types and application. Link budget in free space
  • Transmission lines: reflection coefficient and impedance at the load section and along the line, matching at the generator and/or load section. Lossy transmission lines: equivalent circuit with distributed parameters, power available at the generator and power transfer
  • Metallic waveguides: main features, TE and TM models, cutoff frequency, wavelength and propagation velocity, monomode usage. Dielectric waveguides (fibers): main features



  • C. Riva, G. G. Gentili, Handbook of Electromagnetics, Maggioli Editore (English version)
  • C. Riva, G. G. Gentili, Appunti di campi elettromagnetici, Maggioli Editore (Italian version)


Didactic material

Exams with solutions

Exam of June 27th, 2022

Exam of July 18th, 2022

Exam of September 6th, 2022

Exam of January 24th, 2023

Exam of June 28th, 2023

Exam of July 19th, 2023

Exam of August 29th, 2023

Exam of January 26th, 2024

Exam of February 16th, 2024

Exam of June 28th, 2024


Objectives of the course

The course aims at presenting and describing modern satellite-based communication and positioning systems. Specifically, the first part of the course focuses on key topics and elements that are common to both types of system, such as the propagation of electromagnetic waves in the atmosphere, analog and digital modulation techniques, the link budget. The second part of the course is devoted to different satellite communication systems, whose architecture and key features (e.g. data rate, bit error rate, coding schemes, multiple access schemes) are presented. The last part of the course deals specifically with Global Navigation Satellite Systems (GNSSs), such as the American GPS and the European Galileo, by introducing the basic principles of radio-positioning, the system architectures, the ranging signals, the receiver architectures, and the main applications.


The topics of the course are:

  • Atmospheric electromagnetic wave propagation: ionospheric propagation (physical description of the ionosphere and constitutive equations, total reflection, depolarization, attenuation, delay); tropospheric propagation (ray bending effects, scintillations and multipath, attenuation due to gases, clouds and effects due to rain, models for rain attenuation, depolarization due to rain and ice crystals).
  • Noise in positioning and communication systems: thermal noise, shot noise, noise due to dissipative elements, antenna noise temperature, Low Noise Amplifier, overall noise of a receiver.
  • Modulation techniques: analog modulation (amplitude modulation and associated transmitter block scheme, frequency modulation and associated transmitter block scheme); digital modulation (ASK, PSK, FSK, advanced modulation schemes, bit error rate, bit energy/noise spectral density ratio and its relationship with the bit error rate, Shannon theorem, some elements on information coding).
  • Receivers: the heterodyne receiver; brief description of SDR and of AM and FM demodulators.
  • Space systems: the link budget; different architectures and mission profiles for satellite positioning and communication systems
  • Satellite communication systems: satellite-based communication systems, broadcast (one-way) and telecommunication (two-way) architectures; data relay systems; GEO, MEO, LEO systems.
  • Satellite-based localization and positioning: position estimation techniques based on time of arrival, positioning algorithms, uncertainty and error sources, error correction models, system architectures of modern GNSSs (e.g. GPS and Galileo), space segment (satellite architecture, orbits) and ground segment (monitoring stations, information for system correction/maintenance), augmentation systems, applications of GNSSs.



Electromagnetic wave propagation

  • C. Riva, G. G. Gentili, Handbook of Electromagnetics, Maggioli Editore (also the Italian version is available --> C. Riva, G. G. Gentili, Appunti di campi elettromagnetici, Maggioli Editore)
  • J.A. Richards, Radiowave propagation. An introduction for the non specialists, Springer
  • A. Paraboni, M. D’Amico, Radiopropagazione, McGraw-Hill

Global Navigation Satellite Systems

  • E.D. Kaplan, C.J. Hegarty, Understanding GPS: Principles And Applications (second edition), Editore: Artech House
  • J.-M. Zogg, GPS - Essentials of Satellite Navigation, Editore: u-blox https://zogg-jm.ch/Dateien/GPS_Compendium(GPS-X-02007).pdf


Didactic material

Exams (with solution)

28th of January 2022

14th of February 2022

27th of June 2022

21st of July 2022

25th of January 2023

14th of February 2023

27th of June 2023

24th of July 2023

12th of September 2023

16th of January 2024

6th of February 2024

18th of June 2024

9th of July 2024


Objectives of the course

The objective of the course is to provide the students with the theoretical fundamentals of telecommunication, with particular emphasis on Earth-Space links, to which specific reference is made in the final part of the course. The topics considered are the presentation and discussion of the basic characteristics of the signals constituting the information to be transmitted, the different techniques used to transmit and receive such information, the basic block diagrams of transmitter and receivers analysed in terms of transfer functions of each block and the main characteristics of the different types of antennas. Moreover, the propagation of electromagnetic waves in the real environment, at any frequency, is addressed.


The topics of the course are:

  • Telecommunications basics: Signals classification and characteristics. Analog modulations: amplitude, frequency and phase modulation. Transmitter and receiver block diagrams.
  • Components and circuits: Elementary analog circuits (amplifiers, oscillators, mixers, filters, amplitude and frequency detectors, etc.) and their applications. Elementary digital circuits and their applications. Elementary electronic and microwave components.
  • Antennas: Basic parameters of antennas (gain, directivity function, beamwidth, equivalent area, etc.), main antenna types and characteristics. Fields of application.
  • Electromagnetic wave propagation: Guided propagation (transmission lines, waveguides and fiber optics); radiated propagation (effects of ground, troposphere and ionosphere); dependence of electromagnetic wave propagation on frequency.
  • Earth-space links: Frequency allocation; power and bandwidth requirements; noise and interference. Digital modulation schemes. Links with LEO satellites (brief notes to space probes): effects of the medium. Link budget.



Electromagnetic fields and transmission media

  • C. Riva, G. G. Gentili, Appunti di campi elettromagnetici, Maggioli Editore
  • C. Riva, G. G. Gentili, Handbook of Electromagnetics, Maggioli Editore

Electromagnetic wave propagation

  • J.A. Richards, Radiowave propagation. An introduction for the non specialists, Springer
  • J.E. Allnutt, Satellite to ground radiowave propagation, IET
  • A. Paraboni, M. D’Amico, Radiopropagazione, McGraw-Hill


Didactic material

Exams (with solution)

24th of January 2019

14th of February 2019

26th of June 2019

18th of July 2019

9th of September 2019

14th of January 2020

4th of February 2020

25th of June 2020

17th of July 2020

3rd of September 2020

29th of January 2021

24th of June 2021

15th of July 2021

2nd of September 2021

28th of January 2022

14th of February 2022

27th of June 2022

21st of July 2022

7th of September 2022

25th of January 2023

14th of February 2023

27th of June 2023

24th of July 2023

Objectives of the course

The main objective of the course is to introduce the fundamentals of electromagnetic fields, starting from the sources of the electric and magnetic fileds, to the separate dissertation on the electric and magnetic fields in the static domain, to the treatise of the electromagnetic field in the time varying domain. This course is intended to lay solid foundations for the follow-up courses investigating more in detail the role of electromagnetic waves in ICT applications (e.g. guided and free-space transmission of information). Some elements of such applications are already preliminarily introduced in this course (e.g. transmission lines and plane waves).



  • Basics of scalar and vector fields and vector differential operators. Review of electrostatics and magnetostatics in free space and in materials.
  • Maxwell’s Equations. Definition of time-varying regime. Integral and differential forms of Faraday's law, Ampere-Maxwell’s law and Gauss laws. Poynting’s theorem. Maxwell’s equation in sinusoidal steady state regime.
  • Plane waves. Definition and main properties of plane waves. Plane wave solution of Maxwell’s equations in lossless and lossy media. Polarization of plane waves. Propagation in dielectrics and good conductors. Orthogonal incidence of plane wave on double-layer structure: reflection and transmission.
  • Transmission lines. Transmission line equations and their solution in terms of voltage and current waves and associated fields. Characteristics and input impedances. Incident and reflected waves. Reflection and transmission coefficients and standing wave ratio. Power balance. Lossy transmission lines.


  • Examples of calculation of elettrostatic and magnetostatic fields with elementary sources.
  • Examples of calculation of the electromagnetic field in the time varying domain.
  • Simple problems involving the propagation of plane waves in free space and in different materials.
  • Calculation of the main parameters characterizing tranmission lines.
  • Calulation of the impedance and of power transfer along a transmission line (also lossy ones).

Pre-requisites: trigonometry, calculus with complex numbers, basic notion on vectors, differential and intergal calculus.



  • B. Guru and H. Hiziroglu, Electromagnetic field theory fundamentals, Editor: Cambridge University Press, Year: 2004, ISBN: 0521830168
  • C. Riva, G. G. Gentili, Appunti di campi elettromagnetici, Libreria Cortina.


Didactic material

Exams (no solution)

Years 2015

Years 2016

Years 2017

Exams (with solution)

22nd of January 2018

12th of February 2018

29th of June 2018

18th of July 2018

31st of January 2019

20th of February 2019

8th of July 2019

Problems (with solution)

Induced electromotive force



Il trasferimento di informazione da un punto a un altro: concetti generali. Caratteristiche dei segnali: segnali sinusoidali, segnali modulati. Propagazione guidata e propagazione irradiata: campi di applicazione. Lo spettro elettromagnetico.

Propagazione guidata

Materiali costituenti i mezzi trasmissivi: conduttori, dielettrici e loro proprietà fisiche. Linee a due conduttori: circuito equivalente, onda di tensione e corrente, impedenza caratteristica, potenza disponibile del generatore. Disadattamento, onda diretta e riflessa, coefficiente di riflessione, onde stazionarie. Cenni sui circuiti per l’adattamento. Linee con perdite, circuito equivalente, attenuazione per unità di lunghezza (decibel e neper), dipendenza dell’attenuazione con la frequenza. Diafonia. Tipologie di linee: bifilari, coassiali etc. Cenni su applicazioni della trasmissione lungo linee a due conduttori: telefono, ADSL, CATV, power-line. Guide d’onda dielettriche (fibre ottiche): principi di funzionamento, tipologie in uso, banda passante e attenuazione, campi di applicazione, la rete mondiale di comunicazioni ottiche, i cavi ottici sottomarini. Altre tipologie di linee: guide d’onda metalliche, principi di funzionamento, circuito equivalente, banda passante e attenuazione, applicazioni.

Propagazione irradiata

Il vuoto come mezzo trasmissivo, cosa cambia in presenza dell’ambiente reale. Campi scalari e vettoriali, introduzione alle grandezze specifiche, campo elettrico e magnetico. Introduzione alle equazioni di Maxwell e alla soluzione generale delle onde, densità di potenza, radiazione di una sorgente puntiforme. Le antenne: parametri principali delle antenne. Cenni su applicazioni della propagazione irradiata: collegamenti fissi e mobili, dalle onde lunghe all’ultravioletto.



  • G. G. Gentili, C. Riva, Appunti di onde elettromagnetiche con esercizi, Libreria Clup.


Didactic material

Per i gli esercizi sulle linee di trasmissione (propagazione guidata), fare riferimento ai temi d'esame del corso "Electromagnetic fields" e ai temi d'esame con soluzione riportati qui di seguito.

Temi d'esame con soluzione

A. 2011

A. 2012


Introduzione ai campi elettromagnetici, elettrostatica e magnetostatica

Richiami sui vettori e sulle operazioni vettoriali. Campi scalari e vettoriali. Operatori: flusso e integrale di linea (e circuitazione). Operatori differenziali vettoriali (gradiente, divergenza, rotore). Teorema della divergenza e di Stokes. Proprietà integrali dei campi di tipo gradiente e rotore. Teorema di Helmholtz.

Forza e carica elettrica. Legge di Coulomb. Campo elettrico, densità di flusso elettrico e legge di Gauss. Il potenziale elettrostatico. Relazioni costitutive: campi nei mezzi materiali. Cenni agli aspetti molecolari e alla struttura atomica della materia. Condizioni al contorno sui campi elettrostatici all’interfaccia fra 2 mezzi. Energia elettrostatica. Capacità elettrica 2D e 3D. Concetto di corrente elettrica e legge di Ohm. Resistenza elettrica, legge di Joule. Metodo delle immagini per la soluzione dei campi elettrostatici.

Forze magnetiche e il campo magnetico stazionario. Il campo magnetico nei mezzi materiali

Relazioni costitutive: aspetti molecolari. Condizioni al contorno sui campi magnetostatici all’interfaccia fra 2 mezzi. Energia magnetostatica. Induttanza 2D e 3D, esterna ed interna.

Equazioni di Maxwell

Definizione di regime tempo variante. Legge di Faraday. Flusso dei vettori densità di flusso elettrico e magnetico. Legge di Ampere-Maxwell. Legge di conservazione della carica in forma integrale e differenziale. Relazione costitutive dei mezzi. Anisotropia e dispersione. Condizioni al contorno. Enunciazione dei teoremi di unicità e di Poynting. Regime stazionario sinusoidale: fasori e vettori fasori. Equazioni di Maxwell in regime stazionario sinusoidale.

Introduzione alle onde piane

Funzioni d’onda in regime sinusoidale. L’onda piana: proprietà fondamentali. Onde in mezzi senza perdite. Onde in mezzi con perdite: l’effetto pelle. Riflessione delle onde con incidenza normale e in mezzi senza perdite. Mezzi stratificati e i fenomeni di interferenza. Strati in lambda/4 e in lambda/2.

Linee di trasmissione in regime tempo variante

Linee di trasmissione: distribuzioni dei campi e.m. in una generica sezione. Linee TEM e Quasi TEM. Tensioni e correnti nelle linee di trasmissione. Equazioni delle linee di trasmissione nel dominio del tempo. Onde di tensione e corrente. Velocità di propagazione, impedenza caratteristica e coefficiente di riflessione. Transitorio su una linea di trasmissione.

Linee di trasmissione in regime sinusoidale

Equazioni delle linee di trasmissione in regime sinusoidale. Equivalente circuitale. Onde di tensione e corrente. Velocità di propagazione, impedenza caratteristica e coefficiente di riflessione. Rapporto d’onda stazionaria. Impedenza. Stato stazionario su una linea. Studio dei massimi e minimi dell’inviluppo della tensione lungo una linea di trasmissione. Flusso di potenza. e trasferimento di potenza ad un carico. Il diagramma di Smith.

Linee con perdite

Equivalente circuitale di un tratto di linea con perdite. Significato fisico dei parametri. Resistenza e conduttanza per unità di lunghezza. Linee con piccole perdite. Impedenza caratteristica e costante di propagazione in una linea con piccole perdite. Bilancio di potenza nelle linee con perdite.



  • C. Riva, G. G. Gentili, Appunti di campi elettromagnetici, Libreria Cortina.
  • B. Guru, H. Hiziroglu, Electromagnetics Field Theory Fundamentals, Second Edition, Cambridge.
  • Ramo, Whinnery, Van Duzer, Fields and waves in communication electronics, John Wiley.
  • Ulaby, Fundamentals of Applied Electromagnetics, Prentice Hall.
  • Conciauro, Introduzione alle onde elettromagnetiche, McGraw-Hill.
  • N.N. Rao, Elements of engineering electromagnetics, Pearson.
  • D’Amico, Gentili, Esercizi di campi elettromagnetici, CUSL.


Didactic material


Esercizi di riepilogo elettrostatica e magnetostatica

Eserciziario A. Ratti e M. Savino

Temi d'esame

AA. 2002-2003       AA. 2004-2005       AA. 2005-2006

AA. 2006-2007       AA. 2007-2008       AA. 2008-2009

Temi d'esame con soluzione

AA. 2005-2006       AA. 2006-2007

AA. 2007-2008       AA. 2008-2009


Onde in spazio libero

Richiami sulle equazioni di Maxwell, sulle funzioni d’onda e su alcuni teoremi dell’elettromagnetismo. Equazioni di Maxwell nel dominio del numero d’onda. Onde piane uniformi e non uniformi (onde in mezzi ideali, buoni dielettrici, buoni conduttori, mezzi qualsiasi, onde nei plasmi). Polarizzazione delle onde (polarizzazione lineare, circolare, ellittica). Riflessione e trasmissione delle onde piane (angolo critico, angolo di polarizzazione). Multistrati (effetto tunnel, effetto guidante). Decomposizione di un campo assegnato in onde piane

Onde guidate

I potenziali di Hertz e la propagazione guidata: modi in mezzo omogeneo (TE, TM, TEM). Onde ibride. Velocità di fase e di gruppo (dispersione temporale). La guida d’onda rettangolare. La guida d’onda circolare. Propagazione guidata da uno slab dielettrico: le fibre ottiche (slab lineare, guida circolare a salto d’indice).


I potenziali ritardati e la radiazione elettromagnetica. Il dipolo Hertziano, campi vicini e campi lontani. Diagramma di radiazione e parametri di antenna (cenni).



  • G. G. Gentili, C. Riva, Appunti di onde elettromagnetiche con esercizi, Libreria Clup.
  • D. M. Pozar, Microwave Engineering, J. Wiley.
  • U.S. Inan, A.S. Inan, Electromagnetic waves, Prentice Hall.
  • G. Conciauro, Introduzione alle onde elettromagnetiche, McGraw-Hill.
  • C. A. Balanis, Advanced Engineering Electromagnetics, J. Wiley.
  • R. E. Collin, Field Theory af Guided Waves, IEEE Press.
  • C. G. Someda, Electromagnetic Waves, Chapman & Hall


Didactic material

Temi d'esame

AA. 2004-2005-2006 (Vecchio corso "Onde Elettromagnetiche - B")

AA. 2006-2007

Temi d'esame con soluzione

A. 2010

A. 2011


Objectives of the course

The goal of the course is to provide the students with the theoretical knowledge and the methodologies necessary for modelling, analyzing, and designing wireless links for space-borne systems, both at radio and optical frequencies, in diversified Earth-space scenarios (e.g. Earth observation missions, satellite communications - SatCom, global navigation satellite systems - GNSS). Moreover, the course provides the students with the instruments for understanding and applying the advanced technologies used in modern wireless links. The course offers a balanced compromise between theoretical aspects and practical ones: first, the physical aspects of the phenomena are duly introduced; second, the theory behind them is addressed; third: a practical mathematical framework is derived useful for system design and analysis. The course also includes brief seminars providing an overview on “real world” systems (e.g. experimental measurements) and offers brief practical sessions focused on software tools conceived to support the design of wireless links.



  • Introduction: contents of the course and main protagonists in the history of electromagnetic wave propagation and space-borne systems.
  • The electromagnetic spectrum: frequency bands and spectrum management.
  • Main features of electromagnetic waves (frequency, wavelength, polarization, ...) and electromagnetic characterizations of materials (electric permittivity and magnetic permeability, conductivity, ...).
  • Basic propagation mechanisms at radio frequency and optical wavelengths (Free Space Optics): direct wave, reflected wave, evanescent waves, diffraction and Fresnel’s ellipsoids.
  • Propagation in the ionosphere. Refraction, attenuation, Faraday rotation, phase advance and group delay. Basic principles of radio-positioning in Global Navigation Satellite Systems (GNSS) and impact of the ionosphere on such systems.
  • Propagation in the non-ionized atmosphere (troposphere) and impact on Earth-space (HAPs, LEO, MEO, GEO satellites, Deep Space probes) links. Clear air propagation: refraction and ray bending, attenuation, scintillation, tropospheric scatter. Propagation through clouds.
  • Adverse weather disturbances: attenuation, depolarization, electromagnetic interference due to hydrometeors.
  • Atmospheric and extra-atmospheric noise sources: impact on the signal detection and some concepts on ground-based passive remote sensing.
  • Statistical characterization of the radio channel and system design: the link budget. Basics on fade mitigation techniques (e.g. site, frequency and time diversity, uplink power control, …).


  • Problem solving on all the topics listed above.
  • Presentation and use of the following software tools: propagation of plane waves through multi-layered materials, link budget in clear air, link budget for SatCom systems (including the impact of adverse weather conditions).
  • Mentions to ITU-R recommendation, propagation series.



  • C. Riva, G. G. Gentili, Handbook of Electromagnetics, Maggioli Editore
  • A. Paraboni, M. D’Amico, Radiopropagazione, McGraw-Hill
  • J.E. Allnutt, Satellite to ground radiowave propagation, IET
  • Jean-Marie Zogg, GPS - Essentials of Satellite Navigation, u-blox https://www.zogg-jm.ch/Dateien/GPS_Compendium(GPS-X-02007).pdf


Didactic material

Exams with solutions


Exam of July 1st, 2016

Exam of July 18th, 2016

Exam of September 5th, 2016

Exam of July 7th, 2017

Exam of July 20th, 2017

Exam of September 5th, 2017

Exam of January 22nd, 2018

Exam of June 29th, 2018

Exam of July 18th, 2018

Exam of September 11th, 2018

Exam of June 21st, 2019

Exam of July 8th, 2019

Exam of September 3rd, 2019

Exam of June 19th, 2020

Exam of July 10th, 2020

Exam of September 1st, 2020

Exam of June 18th, 2021

Exam of July 12th, 2021

Exam of August 31st, 2021

Exam of February 17th, 2022

Exam of June 22th, 2022

Exam of July 15th, 2022 - Part 1

Exam of July 15th, 2022 - Part 2

Exam of September 8th, 2022

Exam of June 26th, 2023

Exam of July 25th, 2023

Exam of August 31th, 2023

Exam of June 13th, 2024

Exam of July 2nd, 2024

Problems with solutions

Plane waves