The course introduces the knowledge of the principles of electrical engineering and aims to provide students with the methods for studying electrical circuits and preparatory knowledge for subsequent courses in electronics, automatic and electrical communications.
After a brief mention of the electric and magnetic fields, useful for the introduction of the model with concentrated parameters, the student engineer learns to analyze simple circuits in the time and sinusoidal regime, methods of systematic analysis and fundamental theorems of analysis of networks.
Finally, the typical use of models and methods of electrical circuit analysis for signal and power applications is highlighted.
Knowledge and understanding.
The knowledge acquired during the course, in particular, the link
between the electromagnetic field and the model with concentrated
parameters, the solution methods and the theorems of the electrical
networks allow the student to fully understand the functioning of the
electrical networks, as well as the application and limits of validity
of the circuit model.
Applying knowledge and understanding.
At the end of the course, the student acquires the ability to solve
linear and time-invariant electric circuits both in stationary and
sinusoidal regimes as well as in transient.
Making judgements.
The course also aims to improve critical skills and judgment. In fact,
the student is asked to identify the most appropriate solution methods
in relation to the complexity of the circuit to be analyzed. Moreover,
each time he analyzes an electrical circuit, the student is asked to
verify the correctness of the solution obtained both on the basis of
the approximate knowledge of the expected solution and the comparison
of solutions obtained with different methods (and with IT tools).
Finally, he is invited to critically interpret any anomalies found in
the solution of a circuit. In this way, he acquires certainty of the
result found, an awareness of the functioning of the circuit and is
able to judge autonomously the correctness of the obtained solution.
Communication skills.
The student learns the correct use of the circuit and mathematical
symbols as well as the technical terms and units used in electrical
engineering.
Learning skills.
The study of the subject improves the classification skills of the
engineer student. In particular, by solving the electrical circuits
with the various systematic methods and theorems studied in the theory
of circuits, the student catalogs the circuits in different classes, on
the basis of their topology and the bipoles that compose them, in order
to identify the most efficient method for analyze the circuit itself.
The improvement of the classification capacity and the exercise of the
critical spirit contribute to strengthening the student's ability to
continue the study autonomously after the course of study.
The knowledge to be acquired during the course is the content of the lectures conducted in the classroom by the teacher and - in order to facilitate personal study - the topics are listed in detail in the course syllabus, with explicit references to the parts in which they are covered in the main set texts.
Practical classes and personal training by solving exercises are the means to acquire the ability to apply knowledge. Examples, with the steps necessary to apply the knowledge acquired to the solution of the circuits, are carried out by the teacher in the classroom during the practical classes that follow the explanation of a new topic. Some of the exercises solved by the teacher are also solved by means of a free software for the numerical solution of the electric networks so as to provide students with an alternative way to independently verify the correctness of the results obtained. In order to guide the student, during the personal training phase, to master the tools to be used for the solution of the circuits, at the end of each practical class, a list of recommended exercises (available on the reference books for the exercises or online) is published. In addition, the student is invited to solve the same circuit with different methods, using all the knowledge acquired and all the tools (including IT ones) at their disposal, thus multiplying the value of the single exercise. Finally, the student is encouraged to deepen the topics covered using materials other than those proposed, especially for what concerns the personal study phase, thus developing the ability to apply the acquired knowledge to contexts different from those presented during the course.
To
encourage students to study theory topics and to practice already
during the course, as well as to facilitate the passing of the final
exam in the sessions immediately following the conclusion of the
course, there is an alternative route to the classic exam (typically
consisting of a written test and an oral exam) consisting of:
This route allows students to evaluate if they are up to date with the arguments explained by the teacher and has the advantage of splitting the written exam into two tests to be tackled at different times, ensuring the student has more time available for the solution of the proposed questions.
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.
1. Introductory knowledge.
Scientific notation and order of magnitude. International System of Units (SI); electricalIntroduction to the discipline.
2. Circuit model.
Assumptions, deduction and validity limits of the Circuit model. Electrical elements andrelationships. Nodes, sides and network variables. Kirchhoff's laws and equations.
3. General properties and theorems of electrical networks.
Main properties of an electrical network: zerodimensionality, solvability, linearity, timeEquivalent Network Theorem, Reciprocity Theorem.
4. Bipolar elements.
Adynamic bipoles. Characteristic variables, form and naming of characteristic relationships;capacitance and equivalent inductance.
5. Two-port elements.
Adynamic two-port: characteristic variables, form and naming of characteristic relationships;inductances, equivalent circuit.
6. Graphs and methods of network analysis.
Definition of graph, connected graph, planar graph, mesh, cut set, ring, tree and cotree; treesystematically writing the relevant equations.
7. Time-invariant linear networks.
Transient regime and time domain analysis. Response with zero input: natural frequencies,frequency domain; topological and characteristic equations; network functions; poles and zeros.
8. Networks in sinusoidal regime.
Periodic quantities and their parameters: mean value, rms value. Symbolic representation ofin cascade.
10. Transmission lines.
Assumptions, deduction and limits of validity of the transmission line model; primarylines.
11. Electromagnetism.
Static electric field. Capacitance coefficients, potential coefficients and energy of a conductorTeory
Other books to consult
Exercises (all the texts of exercises are equally good, we report a non-exhaustive list of some texts recommended and available at the library of Engineering).
Subjects | Text References | |
---|---|---|
1 | Introductory knowledge. Introduction to the discipline. | Material provided by the lecturer. 1) XIII-XVII; 3) 1.1-1.6. |
2 | Circuit model. Electrical elements and electrical networks. Kirchhoff's laws and equations. | 1) XIII-XVII; 3) 1.1-1.6. Material provided by the lecturer. |
3 | Elements of graph theory and their application to electrical networks. Tellegen's theorem. | 1) 3.1-3.4, 3.7; 2) 9.1.9.4. *3) 4.1-4.5. *Material provided by the lecturer. |
4 | Systematic methods of network analysis. | 1) 3.5-3.6; 2) 10.1-10.5, 11.1-11.2, 11.4-11.5. |
5 | Power, work and electrical energy; energy classification of elements; passivity. | 1) 1.4; 3) 3.8-3.9. *Teaching material provided by the lecturer. |
6 | Adynamic bipoles. Resistor. Equivalence transformations of networks. Independent generators. | 1) 1.6, 2.1, 4; 2) 2.1-2.2, 2.6, 3.1-3.3; *3) 6.1-6.4. |
7 | Adynamic two-port networks. Ideal transformer, dependent generators. | 1) 6.1-6.4; 2) 8.2-8.3, 17.5-17.6; *3) 7.1-7.6. |
8 | Representations of two-port networks. Reciprocity and symmetry. Interconnection of two-port networks. | 1) 6.1-6.4; 2) 8.2-8.3, 17.5-17.6; *3) 7.1-7.6. |
9 | Use of systematic methods of analysis of electrical networks . | 1) 3.5-3.6; 2) 10.1-10.5, 11.1-11.2, 11.4-11.5. |
10 | Dynamic bipoles. Capacitors and inductors. | 1) 1.7; 2) 2.3-2.4, 2.6; *3) 9.1-9.9. |
11 | Dynamic two-port networks. Coupled inductors. Leakage coefficients. Equivalent circuits. | 1) 6.4; 2) 8.1; *3) 10 |
12 | Ferromagnetic media. Magnetic circuits; calculation of self and mutual induction coefficients. | 3) 24.11, 24.13;*24.14. *Teaching material provided by the lecturer. |
13 | Periodic quantities. Sinusoidal steady-state, phasors, network functions. Frequency response of RC, RL and RLC networks. | 1) 5.1-5.2, 5.4-5.6, 5.8; 2) 7.1-7.6; *3) 2, 14.1-14.4, 14.7-12. |
14 | Energetics of a network in sinusoidal steady-state. Maximum Active Power Transfer Theorem, Boucherot's Theorem. Single-phase rephasing. | 1) 5.3, 5.9; 2) 7.7; *3) 14.5, 14.13. |
15 | Three-phase systems and quantities. Equipotentiality of star centres. Symmetrical and balanced networks. Powers in three-phase systems. Aron's theorem. Forteschue's theorem. | 1) 5.10; 3) 15.1-15.5, 15.7, 15,9-15.10. |
16 | Properties, analysis and solution of an electrical network. Analysis in the time domain. | 1) 7.3; 2) 6.1-6.4. |
17 | Responses in the time domain: properties and calculation. | 1) 7.3; 2) 6.1-6.4. |
18 | Minimum order differential equation. Natural fequencies and stability of a network. Isomorphic regime theorem. | 1) 7.3; 2) 6.1-6.4; 14.1, 14.3-14.4. |
19 | Detailed study of first-order networks. | 1) 2.3; 2) 4.1-4.3. |
20 | Detailed study of second-order networks. | 1) 7.2; 2) 12. |
21 | State of an electricity grid and method of analysing state variables. . | 1) 7.2; 2) 12. |
22 | Laplace's operator method and electrical networks. Analysis in the complex pulsation domain. Network functions; poles and zeros. | 1) 7.4; 2) 13, 15. |
23 | Substitution Theorem, Superposition Theorem, Thevenin-Norton Theorem, Reciprocity Theorem. | 2) 16.1.1, 16.2.1, 16.3.1, 16.4.1. 1) 4.2.3, 4.3, 6.3.1. |
24 | Static electric field. Capacitor bipole. Examples of capacitance calculations. | Teaching material provided by the lecturer. *3) 23.1-32.12. |
25 | Stationary current field. Bipole resistor. Examples of resistor calculations. | Teaching material by the lecturer. *3) 21.1- 21.5; 21.8-21.9;21.11-21.12. |
26 | Stationary magnetic field. Inductor bipole. Calculation examples of self and mutual inductance. | Teaching material by the lecturer. *3) 24.1, 24.3-24.8. |
27 | Quasi-stationary electromagnetic field. Induced currents and skin effect . | Teaching material provided by the lecturer. *3) 24.15-25.22. |
28 | Non-stationary electromagnetic field. Electromotive force, displacement current. | Teaching material provided by the lecturer. *3) 25.1-25.4; 24.23. |
29 | Computational electromagnetism. | Teaching material provided by the lecturer. |
30 | Transmission Line Model. Telegraphers' equations. Lines in sinusoidal steady-state. | Teaching material provided by the lecturer. *3) 27.1-27.2; 27.7-27.9;27.12. |
31 | Teaching material marked with * is intended as in-depth material on the subject. | |
32 | list of exercises | Suggested exercises divided by subject available on the Studium platform. Suggested exercise texts. |
33 | Analysis of elementary resistive networks; calculation of network functions. | |
34 | Application of the method of node potentials to the analysis of resistive networks. | |
35 | Application of the mesh current method to the analysis of resistive networks. | |
36 | Determination of representations of resistive two-port networks. | |
37 | Magnetic circuits and calculation of self and mutual inductances. | |
38 | Analysis of elementary sinusoidal steady-state networks; calculation of network functions. | |
39 | Analysis of sinusoidal steady-state networks using systematic methods; calculation of network functions. | |
40 | Analysis of sinusoidal steady-state networks using systematic methods; calculation of network functions. | |
41 | Calculation of powers and application of theorems for sinusoidal steady-state networks. | |
42 | Calculation of powers and application of theorems for sinusoidal steady-state networks. | |
43 | Analysis of three-phase networks. | |
44 | Analysis of three-phase networks. | |
45 | Time domain analysis of transient networks by means of node potentials and mesh currents methods. | |
46 | Time domain analysis of transient networks using the state variable method. | |
47 | Complex pulsation domain analysis with systematic methods of transient regime networks. | |
48 | Complex pulsation domain analysis with systematic methods of transient regime networks. | |
49 | End-of-course exercise. | |
50 | End-of-course exercise. | |
51 | End-of-course exercise. | |
52 | End-of-course exercise. |