BASIC ELECTRICAL ENGINEERING (Electrotechnics) M - Z

Course Description

This course introduces the theoretical and methodological foundations of electrical circuits and networks. Students will learn circuit modeling techniques and the application of the main analytical methods for the study of electrical circuits under both transient and steady-state conditions (DC and sinusoidal AC). Particular emphasis is placed on sinusoidal steady-state analysis, which provides the essential background for understanding modern energy conversion and management systems.

Learning Outcomes

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

Knowledge and Understanding

• Explain the theoretical foundations of circuit models and lumped-parameter representations.
• Describe the operating principles of linear time-invariant (LTI) electrical networks.
• Understand the behavior of electrical circuits under DC, transient, and sinusoidal steady-state conditions.
• Recognize the role of electrical circuits in energy conversion systems.

Applying Knowledge and Understanding

• Apply systematic nodal and mesh analysis methods to determine voltages, currents, and power in electrical circuits.
• Analyze linear time-invariant electrical networks under DC, transient, and sinusoidal steady-state conditions.
• Determine the dynamic response of first-order and second-order circuits.
• Apply the fundamental network theorems to simplify and solve complex electrical circuits.

Making Judgements

• Select the most appropriate analytical methods according to the characteristics of a given circuit.
• Critically evaluate the correctness of the obtained solutions.

Communication Skills

• Use the technical terminology of electrical circuit theory correctly.
• Present the solution of circuit analysis problems clearly, both in written and oral form, and critically discuss the obtained results.
• Communicate circuit analysis methodologies and results clearly and using appropriate technical language to both specialist and non-specialist audiences.

Learning Skills

• Develop analytical and critical thinking skills through a balanced approach combining theoretical concepts and problem-solving activities.
• Identify common properties shared by different classes of electrical networks.
• Classify engineering problems and adopt effective personal learning strategies to support further studies in advanced engineering topics. 

The course consists of lectures devoted to the presentation of the theoretical foundations of electrical circuits (Direct Instruction) and guided problem-solving sessions with collective discussion of solutions (Interactive Teaching). The practical sessions enable students to apply analytical methods while developing the competencies described in the expected learning outcomes.

Should the course be delivered in blended or distance-learning mode, appropriate modifications may be introduced to ensure full coverage of the syllabus.

Mathematics

• Matrix algebra: systems of linear equations, determinants, transpose, inverse.
• Complex numbers: algebraic, trigonometric, and exponential forms; Cartesian and polar representations; arithmetic operations and roots.
• Calculus: limits, derivatives, and integrals.
• Ordinary Differential Equations (ODEs): nth-order differential equations, first-order systems of ODEs, equivalence between differential equations and systems, and the Cauchy initial value problem.

Physics

• Physical quantities: work, power, and energy.
• Fundamentals of electrostatics: conductors and insulators, electric charge, Coulomb's law, electric field and electric potential, electric field energy and energy density, electric current.
• Fundamentals of magnetism: magnetic field, magnetic permeability, Faraday's law of electromagnetic induction

Fundamental Electrical Quantities

(Lectures: 1 hour)

Lumped-Parameter Circuits and One-Port and Two-Port Elements

(Lectures: 5 hours; Tutorials: 2 hours)

Lumped-parameter model. One-port element model. Lumped electrical networks. Nodes. Kirchhoff's laws. Independent sources. Resistors. Nonlinear resistors. Controlled sources. Ideal transformer. Ideal diode. Power and energy. Series and parallel connections. Voltage and current dividers. Star-delta and delta-star transformations. Thévenin and Norton equivalent circuits.

Systematic Methods for the Analysis of Resistive Networks

(Lectures: 4 hours; Tutorials: 8 hours)

Systematic methods for writing linearly independent Kirchhoff's laws. Circuit solution. Incidence matrix. Tellegen's theorem. Nodal analysis. Mesh analysis. Substitution theorem. Superposition theorem. Thévenin's and Norton's theorems.

Dynamic Analysis of Linear Time-Invariant Circuits

(Lectures: 8 hours; Tutorials: 8 hours)

Energy-storage elements (capacitors, inductors, and coupled inductors). First-order circuits. Examples of second-order circuits: series and parallel RLC circuits. Second-order differential equations and initial conditions. Overdamped, critically damped, and underdamped responses. Particular solution. Steady-state response. State concept. State equations. Minimum-order differential equation. Natural frequencies. Stability.

Sinusoidal Steady-State Analysis

(Lectures: 10 hours; Tutorials: 12 hours)

Contribution to the UN 2030 Sustainable Development Goals

The topics covered in this course directly and indirectly contribute to the development of sustainable technological solutions while promoting high-quality education. In particular, the competencies acquired enable students to understand the operation of electrical systems, providing the foundation for designing efficient technologies for energy conversion and management, thereby contributing primarily to Sustainable Development Goals 4, 7, and 9. Indirect contributions also relate to Goals 11, 12, and 13.

1. Lectures notes (in italian)

2. C.A. Desoer, E.S. Kuh, "Basic Circuit Theory", McGraw-Hill, 1969

The assessment consists of a written examination followed by an oral examination; both components are mandatory.

The written examination lasts 2 hours and consists of solving two problems covering the topics addressed during the course. Admission to the oral examination requires a minimum score of 18/30 in the written examination.

The oral examination assesses the student's theoretical knowledge, ability to establish connections among the different course topics, correct use of technical terminology, and ability to critically discuss the proposed solutions.

The final grade is based on the correctness of the written examination, the knowledge of theoretical concepts, the ability to apply circuit analysis methods, the appropriate use of technical language, and the ability to establish meaningful connections among the topics covered during the course.

Note: Information for students with disabilities and/or specific learning disorders (SLD)

To ensure equal opportunities and in compliance with current regulations, interested students may request a personal meeting to plan any necessary compensatory measures and/or dispensations, based on educational objectives and specific needs. Students may also contact the designated CInAP representative.

• Series and parallel RLC circuits.
• Natural frequencies.
• Sinusoidal steady-state analysis.
• Power under sinusoidal steady-state conditions.
• Circuit stability.
• Nodal analysis.
• Mesh analysis.
• Tellegen's theorem.
• Boucherot's theorem.
• Thévenin's and Norton's theorems.
• Maximum active power transfer theorem.
• Two-port networks.
• Phasors.
• Circuits operating under sinusoidal steady-state conditions.
• Fundamental theorem of sinusoidal steady-state analysis.
• Impedance and admittance.

Learning Materials

Worked examples and collections of recommended exercises are available on the Studium learning platform.