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Informazioni aggiuntive

Course Curriculum CFU Length(h)


Professional aims: Knowing how to model an electromagnetic device using the lumped circuit representation; ability to analyze simple passive and active filters. Knowing how to analyze symmetrical balanced and unbalanced three-phase systems. Knowing how to determine fault currents in a three-phase circuit. Knowing how to determine the circuit parameters of coupled circuits.
Disciplinary Objectives: Knowing how to analyze a lumped circuit in steady state, sinusoidal and periodic behavior. Derive the complete response of a circuit in the time domain and in the domain of the Laplace variable.
Expected knowledge: Knowledge about the constitutive relations of the lumped components, the fundamental relations of circuit theory, the theorems and methods for the analysis of circuits in steady state, the symbolic method, the theorems and methods for the analysis of circuits in sinusoidal regime, knowledge on the approach with the state variables for the analysis of the dynamic behavior of a circuit, on the use of the Laplace transform for the circuit analysis, and knowledge on frequency analysis of a circuit. Knowledge of the theory of electromagnetism. Knowledge of the principle of operation of induction machines and the first-order model of the single-phase transformer.
Expected abilities: ability to apply the theorems and methods for the analysis of lumped circuits in steady state, and sinusoidal regime, and be able to analyze the dynamic behavior of a lumped circuit. Knowing how to perform frequency analysis of circuits and to recognize the type of a passive and active filter. Knowing how to analyze a magnetic circuit. Knowing how to determine the circuit parameters of mutually coupled circuits. Knowing how to analyze a single-phase transformer starting from the nominal data. Ability to clearly express technical concepts.
Expected skills: Being able to assess the applicability of circuit theory and build its lumped parameter model for devices of medium complexity. Knowing how to solve the corresponding model with the circuit theory.
Making judgments: develop the ability to critically evaluate the results of the circuit.
Learning skills: knowing how to integrate knowledge from different sources in order to achieve a broad understanding of the issues related to the analysis of electric and magnetic circuits and devices.


Knowledge: An adequate knowledge of the fundamental methodological aspects of the basic sciences (calculus, geometry, physics). In particular, knowledge of: matrix algebra in the real and complex domain, derivatives, integrals, ordinary differential equations, Fourier series, Laplace transforms, the basic laws of electromagnetism.
Skills: Be able to solve systems of algebraic equations in real and complex algebra, how to derive and integrate functions, ability on solving systems of differential equations, knowing how to apply the Laplace transforms and anti-transforms. Knowing how to formulate the relationships between the electrical quantities in the resistors, capacitors, and inductors.
Skills: The skills acquired so far are essential to the understanding, interpretation, critical analysis and troubleshooting of medium difficulty circuits using the theory of circuits.
It is recommended to have passed the following exams: Mathematics 1, Mathematics 2, Applied and computational Mathematics and Physics 2.


First module: I° semester 60 hours
Lumped circuits (16 hours)
Physical quantities and electrical circuits, Assumptions of validity, voltage and current, first and second Kirchhoff's laws, Components and ports, descriptive variables, power and energy, conventions. General properties of components and circuits. Resistor, capacitor, inductor, independent voltage and current controlled generators, operational amplifier, mutually coupled inductors, ideal transformers. Real components. Components in series and in parallel, star-delta transformation.
Staty state circuits (20 hours)
Graph of a circuit and topological notions, fundamental methods of analysis: links and nodes. Tellegen's theorem and the superposition principle. Thevenin's and Norton's theorems. Theorem of maximum power transfer.
Circuits in sinusoidal regime (24 hours)
Sinusoidal functions and phasors. Properties phasor and derivative of a phasor. Analysis in the phasor domain. Impedance and admittance. Network Analysis in sinusoidal regime. Theorems. Power and energy. Passive bipoles. Conservation of complex power (Boucherot). Theorem of the maximum power transfer. Addictivity of powers. The problem of power factor correction. Two-ports.
Second module: II semester, 60 hours
Frequency response. Resonant circuits. Passive filters. Active filters.
Circuit analysis in dynamic operation (30 hours)
Analysis in the time domain, Input / output relationships and state equations. Examples of first order and second order circuits. Electric signals: unit impulse, unit step, sinusoidal signal. Analysis in the domain of the Laplace variable and Inverse Laplace. Network Features: response of the circuit, impulse response, properties of network functions. Stability.
Three-phase systems (10 hours of lectures and 4 exercise)
Polyphase systems and symmetrical three-phase systems. Connection of generators and loads. Terns of sequence. Symmetrical and balanced three phases networks. Generalized Thevenin's theorem. Unbalanced three-phase networks. Power in three-phase loads. Measurements in three-phase systems. Aron insertion. Measures in unbalanced three-phase loads. Power factor correction of three-phase loads. Principle of decomposition. Analysis of three-phase systems using the theory of symmetrical components. Calculation of short-circuit currents.
Magnetic circuits (10 hours of lectures and exercise 6)
Fundamentals of the theory of stationary magnetic fields. Hysteresis and hysteresis losses. Normal curve of magnetization. Inert magnetic circuits. Analogy between electric and magnetic circuits. Direct problem and inverse problem. Calculation of the parameters of the mutual inductance. Equivalent circuits of mutually coupled circuits. Inductive transformer. Real transformer. Equivalent circuit of the real transformer. Open circuit and short-circuit tests of the transformers. Calculation of the parameters of the equivalent circuit of the first-order single-phase transformer. Load operation of the transformer. Theorem of Galileo Ferraris. Rotating magnetic field. Electromagnetic actions of rotating magnetic fields. Principle of operation of rotating machines.

Teaching Methods

Teaching is organized in a blended way with both lectures and classroom exercises and with the support of video lessons. Tutoring activities are also organized.
The on-line teaching is composed by two components: the “front teaching” and the “interactive teaching”.
The “front teaching” is divided into several modules, each of them sub-divided into units. Each unit is organized in order to fulfill the specific educational goal and can be constituted by: video lecture supported by slides, videos and animations; slides and videos mainly aiming to present application of the theory and examples; test with automatic check which will be useful for auto-evaluation by the students themselves.
The “interactive teaching” is the moment of a direct contact between the students and the teacher or the tutor by means of e-mails, forum, video-conferences.
All video-lectures and test are available on-line in an asynchronous manner by means of the most common devices (PC, tablets, smart-phone) and using the most common softwares (Explorer, Crome, Mozilla, etc).
Furthermore it is possible to download some specific material such as slides, tables, exercises.

Verification of learning

The manner in which it is ascertained the effective acquisition by the students of the expected learning outcomes are:
Specific self-assessment questionnaire proposed in the classroom and regarding the prerequisites.
Self-assessment of knowledge, skills and competences acquired through interactive exercises in the classroom with the teacher and support staff in the classroom.
Evidence of learning during the year: 2 intermediate writing tests consisting in solving a series of exercises on different parts of the program of the course.
Written and oral examination during the sessions (fortnightly following the Faculty Academic Calendar). The written test consists in solving a series of exercises on the program of the course. This method (Written and oral examination) is designed to ensure the effective acquisition by students of knowledge, skills and abilities consistent with the educational objectives of teaching as well as to increase his communication skills.

The final score is out of thirty, weighing each time the rating attributed to the different exercises according to the commitment required for their solution both in terms of content and computational complexity.
The rating 18/30 is granted when knowledge / skills of matter are at least elementary, the 30/30 rating, with possible honors, is granted if the knowledge is excellent.


1. Alexander, Sadiku, Circuiti elettrici, Mc Graw Hill
Solutions of the exemples proposed in the text are available at the address
2. Perfetti, Circuiti Elettrici, Zanichelli
3. Rizzoni, Elettrotecnica, Principi ed Applicazioni, McGraw Hill
4 Civalleri, Elettrotecnica, Levrotto e Bella, Torino
5. Repetto, Leva, Elettrotecnica, CittàStudi Edizioni
6. Biorci, Fondamenti di Elettrotecnica, UTET

More Information

Slides and lecture notes are available on the web site At the same site the traces of the exams are available.

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