ING-IND/31 - 9 CFU - 2° Semester

Teaching Staff


Learning Objectives

The course aims to provide students with the knowledge of the theoretical and methodological bases of the circuit model, as well as the methods of analysis and the main theorems of electrical networks, operating both in transient and sinusoidal conditions. Particular emphasis is given to the study of the latter, in consideration of the fact that its knowledge is essential for the understanding of numerous and important topics falling within the field of industrial engineering, such as the operation of machines, plant drives and electrical measuring instruments, as well as that of power electronic circuits and industrial automation systems. The course also provides a panoramic description of the most important applications of stationary and quasi-stationary electric and magnetic fields, magnetic circuits, three-phase networks and transmission lines.

Knowledge and understanding.

A knowledge of significant conceptual importance that the students acquire during the course is the understanding of the complementarity relationship existing between the field formulation, based on the fundamental laws of the electromagnetic field, and the circuit one, based on the electric network model called concentrated parameters or , with different diction, zero-dimensional model. Both formulations are in fact widely used to analyze the operation of numerous electrical devices and systems, as well as to carry out their design. Another important acquisition of students is represented by the learning of methods of analysis of electrical networks having characteristics of generality, systematicity and efficiency, as well as the main theorems of electrical networks. This body of knowledge allows them to fully understand the operation of electrical networks, as well as the fields of application and the limits of validity of the circuit model. It is therefore well understood that knowledge of these topics is essential for analyzing new problems and developing original solutions.

Applying knowledge and understanding.

Among the main skills acquired by the student at the end of the course is that of knowing how to analyze linear and time-invariant networks operating both in the stationary and sinusoidal regimes and in the transient one. These skills are essential for the understanding of numerous applications falling within the area of Industrial and Information Engineering, since these applications are the subject of specialized in-depth studies in courses such as, for example, Automatics, Electronics, Power Electronics, Theory of Signals, having said knowledge a strong interdisciplinary value.

Making judgements.
The course also intends to stimulate and increase the ability to exercise the student's critical and judgment skills. In fact, the identification of the most appropriate strategy for solving a given exercise, in relation to the type of questions formulated and the characteristics of the network to be analyzed, requires the student to carry out a careful examination of the problem and a reflection on the knowledge already acquired. apt to solve it. Once the solution has been obtained, the student is also asked to verify the correctness of the solution obtained both on the basis of the expected result, even approximate, and through the comparison of the result obtained using a different method of resolution using, if necessary, also computer tools. A further source of acquiring independent judgment is the ability to provide an explanation for possible initially unexpected results, which further contributes to improving the understanding of the functioning of the electrical network studied and to develop in the course of preparation for the teaching exam, the ability to formulate hypotheses on the behavior of a network, albeit having non-exhaustive information on it.

Communication skills.
One of the results of the course is the learning of the correct use of both the symbology and circuit nomenclature and the mathematical tools and physical knowledge learned in the preparatory courses, necessary for the resolution of specific exercises carried out in class or assigned to the exam tests. . During the lessons, particular attention was obviously dedicated to learning the units of measurement of electrical quantities and their use. A significant part of the theoretical results of the course are demonstrated, further contributing to increasing the understanding of the results themselves and their implications, as well as their appropriate and flexible use in solving the exercises. All this stimulates and advances the student's communicative ability, enabling him to communicate clearly and without uncertainty both with subjects who are cultured in the discipline and with subjects who are not, providing both categories with valid arguments.

Learning skills.
The study of electrical engineering, traditionally and equally divided between the acquisition of concepts and theoretical results and the progressive increase in the ability to resolve electrical networks, leads to an improvement in the student's ability to think and learn. Specifically, the analysis of electrical networks having very different structural and constitutive characteristics, involves the student's refinement of the ability to recognize the general properties of the network under study, as well as identifying the most suitable solution strategy. All this determines an increase in the ability to classify problems and the strengthening of the ability to identify one's own and effective method of study, in relation to the nature of the problem, certainly useful in the continuation of studies.

Course Structure

The knowledge to be acquired during the course is the content of the lectures held in the classroom by the teacher and the topics are listed in detail in the course program, with explicit references to the parts in which they are treated in the recommended texts. The exercises carried out by the teacher in the classroom during the exercises that follow the explanation of a new topic and the personal ones carried out by the student are the tool to acquire the ability to apply the knowledge learned. The student is also encouraged to deepen the topics covered, using materials other than those proposed, especially as regards the personal exercise phase, thus developing the ability to apply the acquired knowledge to contexts different from those presented during the course. If the teaching is given in a mixed or remote mode, the necessary changes may be introduced with respect to what was previously stated, in order to respect the program envisaged and reported in the syllabus.

Detailed Course Content

Maxwell's equations; continuity equation; constitutive equations.

Stationary current field; fields J and E; electric conductibility; scalar potential; Laplace equation; resistance of a resistor.

Electrostatic field; fields D and E; dielectric constant; Poisson equation; capacity of a capacitor.

Magnetostatic field; fields B and H; magnetic permeability; potential vector.

Circuits with lumped parameters, voltage and current, Kirchhoff's laws.

Resistors, capacitors, inductors, independent generators.

Coupled inductors, ideal transformer; dependent generators.

Magnetic circuits, auto and mutual inductances.

Graph of a circuit, nodes and sides; Tellegen's theorem; rings and links, cutting sets; node potentials method; ring currents method, mesh currents method.

Theorems on electric networks: substitution theorem, superposition of effects, Thevenin and Norton equivalent network.

Linear and time-invariant circuits; minimum order differential equation; initial conditions; equations of state.

Theorems on electric networks: substitution theorem, superposition of effects, Thevenin and Norton equivalent network.

Linear and time-invariant circuits; minimum order differential equation; Natural frequencies. Steady state and transient response, zero-state and zero-input response; impulse and step responses; integral of convolution.

Circuits in periodic regime; Fourier series. Laplace transform, network functions, poles and zeros, reciprocity theorem.

Method of state variables.

Circuits in sinusoidal regime; phasors; impedances and admittances; active, reactive, complex, apparent power; single-phase power factor correction.

Boucherot's theorems and the maximum active power transfer.

Three-phase three and four-wire circuits; line and phase voltages and currents; symmetrical and balanced three-phase circuits; equivalent single-phase circuit; power in three-phase circuits; Aron advert.

Two-port elements. Impedance, admittance, hybrid and transmission matrices. No-load and short-circuit impedances, iterative impedances, image impedances, characteristic impedance. Reciprocity and symmetry of a double bipole.

Star-delta transformation. Interconnection of double bipoles: in cascade, in series, in parallel, in series-parallel.

Transmission lines, telegraph equations; characteristic impedance, propagation constant; two-port transmission line; reflection coefficient. Line adapted.

Quasi stationary electromagnetism, skin effect, depth of penetration.

Electromagnetic waves; radiation and scattering.

Textbook Information


1) M. D’Amore, "Elettrotecnica", Ingegneria 2000, Roma, 1994.

2) C. A. Desoer, E.S. Kuh, "Fondamenti di Teoria dei Circuiti", Franco Angeli, 1969.

3) P.P. Civalleri, "Elettrotecnica", Levrotto & Bella, tomo I e II, Torino, 1998.

4) G. Someda, “Elementi di Elettrotecnica Generale”, Patron Ed. (discontinued available in the Engineering and Architecture library).

5) V. Daniele, A. Liberatore, R. Graglia, S. Manetti, Elettrotecnica, Monduzzi Editore (discontinued available in the Engineering and Architecture library).

6) S. Ramo, J. R.Whinnery, T. Van Duzer, Campi e onde nell'elettronica per le telecomunicazioni, Franco Angeli.


1) A. Laurentini, A.R. Meo, R. Pomè, Esercizi di elettrotecnica, Levrotto&Bella.

2) G. Marchesi, P.L. Mondino, C. Monti, A. Morini, Esercizi di elettrotecnica, Libreria Cortina.

3) S. Bobbio, Esercizi di elettrotecnica, CUEN.

4) J.A. Edminidter, Circuiti elettrici, coll. Schaum (1975), McGraw-Hill.

5) J. O’Malley, Basic Circuit Analysis (Second Edition), coll. Schaum's Outlines, McGraw-Hill.

6) S. Alfonzetti, "Esercizi di Elettrotecnica", 2016 (available online on Studium)

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