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CODE 111150
SEMESTER 1° Semester
Propedeuticità in ingresso
Per sostenere l'esame di questo insegnamento è necessario aver sostenuto i seguenti esami:
MODULES Questo insegnamento è un modulo di:



The aim of the course is to provide students of cultural and practical competence of advanced electric circuit analysis models (transient analysis, solved in time and frequency domain through Laplace transform, and three phase circuits).


The aim of the teaching is to enable Students to master, both theorically and practically, the advanced knowledge necessary to study and solve Circuit Models, with particular attention to power aspects.

The analysis is developed in Transient and Steady State AC Three-Phase regimes. Furthermore, the appplication of Laplace Transform to the solution of Linear Circuit is described.

At the end of the teaching, the Student shall have correctly understood the above described concepts of Electric Circuit Analysis, and shall be able to correctly formulate their solution, arriving, when possible, to determine an analytical solution.


Theory lectures and related exercises, for a total of 6 credits. The teaching is held during the first semester.


Typical waveforms for Circuit Problems.

Unitary step functions. Finite time impulse. Unitary slope function. Dirac impulse function, and distributions. Integral and differential relationships among elementary
functions. Construction of stepwise continuous functions as combination of elementary functions. Sinusoidal waveforms. Periodic waveforms. Alternate, odd,
even, and with half-waveform symmetry. Fourier series: harmonic functions, their definition and main properties.

Dynamic Circuit Equations, and their solution.

The solution of Linear Ordinary Differential Equations with constant coefficients. General and Particular Integral, initial conditions, characteristic polynomials. Solution of simple first-order R-C or L-R Circuits. Behaviour of inductors and capacitors during sudden variations of state variables. Circuit of second order with Inductors and Capacitors. Taxonomy of the roots of characteristic polynomial, and their relationship with output waveforms. Natural response and forced response. Example of solution of simple dynamic circuits. Introduction to circuit simulators. Laplace Transform and its application to the solution of linear circuits.


Three-phase circuits.

Definitions and reasons leading to introduce three-phase circuits. Three-phase circuits with balanced (3 conductors) or unbalanced (4 conductors) load. Phase and line voltages. Symmetric/unsymmetrical systems. Balanced/unbalanced loads. Positive, negative, zero sequences. Phase and line currents. Power in three-phase circuits. Solution of simple circuits. Harmonic content of voltage and current in three-phase circuit. Unbalanced circuits. Examples of solution of three-phase circuits, both balanced and unbalanced.


  • M. Brignone, M. Nervi: “Dispense del corso” (Lecture Notes)

Besides the books in Bibliography, available in Department Library, on AulaWeb are available copies of written examination problems, with their solutions.

Reference (for OPTIONAL study deepening on specific subjects)


  • M. Repetto, S. Leva: “Elettrotecnica – Elementi di Teoria ed Esercizi”, 3^ edn, Città Studi Edizioni, Torino, 2022
  • L. Verolino: “Elementi di Reti Elettriche”, 1^ edn, EdiSES, Napoli, 2019

More oriented towards circuit analysis for signal applications:

  • C. K. Alexander, M.N.O. Sadiku: “Circuiti elettrici” V edn., McGraw Hill Italia, 2017.
  • G. Rizzoni: “Elettrotecnica – Principi e applicazioni”, III edn., McGraw Hill Libri Italia, 2018.

For further theoretical study:

  • C.A. Desoer, E. S. Kuh: “Fondamenti di teoria dei circuiti”, 18^ edn, Franco Angeli, Milano, 2010.



Class schedule

The timetable for this course is available here: Portale EasyAcademy



The examination of Circuit Complements is based on two partial written tests held during the teaching (one about Transient regime, and the other about Three Phase Steady State AC regime) that the Student must both solve and one oral discussion, lasting about 30 minutes, after the end of the teaching. In case the Student was absent to one partial test, or the result was not sufficient, the examination will be based on a written test comprising the complete program of the module. The marking will be organized as follows: max. 14 points for the written examination (both for the two partial tests, and for the complete written examination), max. 17 points for the oral examination. To be admitted to the oral examination, the marking of written test (partial or complete) must be at least 8/14. The final marking is the sum of the marks of written and oral examinations.


In written exams, the assessment is done by verifying the ability to obtain a correct solution of some applicative problems regarding all the content of the course; in oral exams are verified: the correct understanding of some theoretical subjects regarding all the content of the course, the correct use of technical language, the ability to critically examine the presented subjects and the successful learning of the technical competence necessary for the fruitful continuation of studies.


Students who have valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework and exams, should speak both with the instructor and with Professor Federico Scarpa (, the School's disability liaison.

Agenda 2030 - Sustainable Development Goals

Agenda 2030 - Sustainable Development Goals
Quality education
Quality education
Affordable and clean energy
Affordable and clean energy