ELETTROTECNICA A - L

Course Description

This course introduces the theoretical and methodological foundations of electrical circuits and networks. Students will learn modeling techniques, analytical methods, and the application of key theorems for the study of circuits under transient and steady-state (DC and AC sinusoidal) conditions. Special emphasis is placed on sinusoidal steady-state analysis, which is essential for understanding modern energy conversion and management systems. Applications of static and quasi-static electromagnetic fields, magnetic circuits, and three-phase networks are also covered.

Learning Outcomes

Upon successful completion of the course, students will be able to:

Knowledge and Understanding

• Explain the theoretical basis of circuit models and lumped parameter representations.
• Apply analytical methods to solve basic electrical circuits.
• Understand the behavior of linear time-invariant circuits in transient and steady-state operation.
• Identify the role of circuits and components in energy conversion, management, and utilization.

Applied Knowledge and Skills

• Analyze linear time-invariant networks in transient, steady-state, and sinusoidal regimes.

Independent Judgment

• Select appropriate solution methods for different circuit types.
• Critically evaluate the validity of obtained solutions.

Communication Skills

• Use standard circuit symbols and technical terminology in electrical engineering.
• Apply mathematical and physical tools to formulate and solve electrical problems.
• Communicate clearly and confidently with professionals in electrical engineering and energy-related fields.

Learning Skills

• Develop reflective and analytical thinking through a balanced approach to theory and problem-solving.
• Recognize general properties across different electrical networks.
• Classify problems and adopt effective personal study strategies, useful for advanced engineering studies.

The course will be delivered through lectures, aimed at providing theoretical foundations, and problem-solving sessions, designed to develop students’ ability to analyze electrical circuits.

In the case of blended or online delivery, appropriate adjustments may be made to ensure full alignment with the planned syllabus.

The course is taught in Italian.

Mathematics

• Matrix algebra: systems of linear equations, rank, determinant, transpose, inverse, sum, product.
• Complex numbers: algebraic, trigonometric, and exponential forms; polar and Cartesian notation; operations and roots.
• Calculus: limits, derivatives (including higher-order), indefinite integrals.
• Ordinary Differential Equations (ODEs): nth-order equations, systems of first-order ODEs, equivalence between equations and systems, Cauchy problem.

Physics

• Physical quantities: work, power, energy.
• Fundamentals of electrostatics: conductors/insulators, electric charge, Coulomb’s law, electric field and potential, Gauss’s theorem, electric field energy and energy density, dielectric constant, current.
• Fundamentals of magnetism: magnetic field, permeability, Faraday’s law of induction, Lenz’s law.

Attendance is not mandatory, but it is strongly recommended for successful completion of the course.

Basic Quantities (Lecture: 1 hour)

Lumped-parameter circuits and one-port and two-port elements. (Lectures: 3 hours; Exercises: 3 hours). Lumped-parameter model. Two-terminal (dipole) model. Lumped-parameter network. Nodes. Kirchhoff’s laws (KVL, KCL). Independent sources. Resistors. Nonlinear resistors. Controlled sources. Ideal transformer. Ideal diode. Capacitors. Inductors. Power and energy.

Interconnection of Two-Terminal Elements and Equivalent Transformations(Lectures: 2 hours; Exercises: 3 hours) Series and parallel connections.  Voltage and current dividers. Star-delta (Y-Δ) and delta-star transformations. Thevenin and Norton equivalents.

Systematic Methods for the Solution of Static Electrical Networks. (Lectures: 8 hours; Exercises: 10 hours) Systematic methods for writing linearly independent KCL/KVL equations. Circuit solution methods. Incidence matrix. Node analysis. Mesh analysis.

Dynamic Analysis of Linear Time-Invariant Circuits (Lectures: 8 hours; Exercises: 10 hours) First-order circuits. Examples of second-order circuits: RLC series and parallel. Second-order differential equations and initial conditions. Overdamped, critically damped, and underdamped cases. Particular solution. Steady-state solution. Concept of state. State equations. Minimum-order differential equation. Natural frequencies. Stability.

Sinusoidal Steady-State Analysis (Lectures: 8 hours; Exercises: 10 hours) Phasors. Circuits in sinusoidal steady state.Fundamental theorem of sinusoidal steady state.First-order circuits in sinusoidal regime.Kirchhoff’s laws and branch equations with phasors.Impedance and admittance. Power and energy in sinusoidal regime. Complex power.

Network Theorems (Lectures: 3 hours; Exercises: 2 hours) Tellegen’s theorem. Boucherot’s theorem. Substitution theorem. Superposition theorem. Superposition in sinusoidal regime. Thevenin’s and Norton’s theorems. Maximum power transfer theorem.

Multiport Elements (Lectures: 2 hours; Exercises: 3 hours). Two-port networks. Representations of two-port networks. Reciprocity in two-port networks. Interconnection of two-port networks. Coupled inductors.

Three-Phase Systems (Lectures: 2 hours; Exercises: 3 hours)

Introduction to the Laplace Transform (Lectures: 1 hour; Exercises: 1 hour) The Laplace transform and its main properties.Kirchhoff’s laws and branch equations in the Laplace domain.Impedance and admittance of resistors, capacitors, and inductors. Transfer function.

Overview of Circuits and Systems for Energy Generation, Storage, and Conversion (Lectures: 2 hours)

Overview of Electrical Safety (Lectures: 2 hours)

Contribution of the course to the Goals of the 2030 Agenda for Sustainable Development
The topics covered in the course and the acquired knowledge are directly or indirectly aimed at the development of sustainable technological solutions, as well as contributing to a high quality education, in accordance with Goals 4, 7, 9, 11, 12, 13 of the 2030 Agenda for Sustainable Development.

The examination consists of a written test and an oral test (both components are mandatory).

The oral test includes the discussion of the written test and additional questions covering parts of the syllabus not addressed in the written examination.

Assessment may also be conducted online, should circumstances require it.

Series and parallel RLC circuits.
Natural frequencies.
Sinusoidal steady state.
Power in sinusoidal steady state.
Circuit stability.
Node analysis.
Mesh analysis.
Tellegen’s theorem.
Boucherot’s theorem.
Thevenin’s and Norton’s theorems.
Maximum active power transfer theorem.
Two-port networks.
Phasors.
Circuits in sinusoidal steady state.
Fundamental theorem of sinusoidal steady state.
Impedance and admittance.
Circuits for modeling electrical machines for energy conversion.
Protection against direct and indirect contact.

Examples of solved exercises and lists of recommended practice problems are available on the Studium platform.