ING-IND/31 - 9 CFU - 1° Semester

Teaching Staff


Learning Objectives

The course contents is addressed towards basic circuit theory, together with an overview of electromagnetic fields formulations used to solve basic static and time-varying electromagnetic problems arising in an engineering context. Fundamental concepts used in electronics, communications, electrical and electronic measurements, control theory are also introduced.

Knowledge and understanding

The student will learn the basic engineering methodologies, through which he will build the specific skills of the course.

Applying knowledge and understanding

At the end of the course the students will be able to solve circuits in time and frequency domains using the most appropriate circuital analysis methodology.

Making judgements

The exercises are aimed at developing critical skills and autonomous paths on the basis of available data

Communication skills

Several examples are given aimed at properly communicating results

Learning skills

The training course is structured so that further studies in this area can be autonomously undertaken with great ease.

Course Structure

Classroom lectures and numerical exercises aimed at developing circuital analysis skills

Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.

Detailed Course Content

Lumped circuits

The lumped circuital model: Voltage and Current. Idealized electrical components. Kirchhoff's Current and Voltage Laws.


One and two port electrical components

Electric power and energy, passive and active elements: independent Current and Voltage sources, Linear time-invariant one and two port elements: resistors, capacitors, and inductors, ideal transformer, coupled inductors, dependent sources. Simple networks: Voltage division of series components, Current division of parallel components Equivalent circuits: Series & Parallel connections for one port components Star-Delta & Delta-Star Transformations. Nonlinear and Time-varying components: ideal diode, ideal circuit breaker


First and second order linear time-invariant circuits.

RC, RL and RLC circuits. State variables. Differential equations and initial conditions. Natural Frequencies..Zero-input, zero state and complete response. Step and impulse reponses. Convolution integral .


Circuit analysis and network theorems

Network graphs and Tellegen's theorem. Nodal and mesh analysis Node Voltage and Mesh Current Methods. Substitution Theorem. Superposition theorem. Norton & Thevenin theorem.


Alternating currents circuits

Alternating Current (AC), Voltage, sinusoidal Waveforms, Frequency, Period, Phase Angle of sinusoidal Waveforms Phasor (Vector) Diagram & Complex Numbers for AC Circuits Analysis. Impedance and admittance concepts. Active and reactive Power. Complex Power and Apparent Power Boucherot Theorem, Power Factor Correction. MTP Theorem. Resonant circuits. Periodic Waveforms, Fourier Analysis for linear circuits

Three-phase circuits: Three and four wires star and delta configurations. Three-phase circuit analysis and Millmann formula. Three-phase power and Aron's theorem.


Two port networks

Representation of linear time-invariant two port networks. Two port networks interconnections. Reciprocity theorem.


Electromagnetic fields

Electrostatic and magnetostatic fields and applications. Laplace and Poisson Equations. Magnetic Circuits. Time-varying electromagnetic fields electromagnetic potentials, Poynting theorem homogeneous and non-homogeneous wave equations, radiation, Hertz’s dipole, transmission lines.

Textbook Information

1. C.A. Desoer, E.S. Kuh , Fondamenti di Teoria dei Circuiti, Franco Angeli Editore,

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

3. R.Perfetti, Circuiti Elettrici, Zanichelli.

4. J.A. Edminister, Circuiti Elettrici, coll. Schaum's, McGraw-Hill.

5. Ramo, Whinnery, Van Duser, Campi e onde nell’elettronica per le comunicazioni Franco Angeli Editore

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