CIRCUIT THEORY
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- Versione italiana
- Academic year
- 2017/2018
- Teacher
- GIANLUCA SETTI
- Credits
- 9
- Didactic period
- Primo Semestre
- SSD
- ING-IND/31
Training objectives
- This is the first class to systematically tackle the study of electric phenomena and exhaustively examine all basic elements which compose an electrical or electronic circuit. The main objective of the class is to offer the fundaments for the study of electric and electronic circuits and is therefore a cornerstone for any other class in the domain of circuits or systems for the areas of electronics, automatic controls, telecommunications and computer engineering.
The main knowledge acquired ad the end of the class is:
- fundamental relationship of circuit theory (Kirchhoff's laws);
- principal techniques for evaluating electrical variables (currents, voltages, and electric power) in circuits composed by multi-terminal elements;
- model of all electrical bipols (resistor, capacitor, inductor, independent voltage and current sources) and of the principal multipoles (transformer, gyrator, voltage/current controlled voltage/current sources, operational amplifier)
- methods for analyzing linear and (in some selected cases) nonlinear a-dynamical (resistive) and dynamical (that is with reactive elements) circuits that operated in DC, transient and sinusoidal regimes.
The principal skills (in terms of capabilities of applying the knowledge acquired) are:
- analyze the behavior of any linear circuit operating in DC, AC or transient conditions;
- analyze circuits in DC conditions containing op-amps;
- identify design constraints that determine the value of the different parameters of a simple electrical and electronic circuits. Prerequisites
- It is necessary to possess knowledge of the following topics from the classes of “Fundaments of Automatics”, “Geometry and Algebra” “Statistical Methods for Engineering” and “Mathematical Analysis II”:
- Stability Theory, poles of a transfer functions;
- matrices, vectors and elementary operations, linear systems and their solutions;
- solutions of systems of differential equations of first order;
- random variables and probability density. Course programme
- The course includes 90 hours of teaching divided between theoretical lectures and exercises. More specifically, 67 hours are of lectures and 18 hours are of classroom exercises, while the remaining 5 hours are of experimental tutorials in the laboratory. The hours of lectures are divided as follows:
1 Electrical variables
Kirchoff's current and voltage laws. Bipoles and multipoles. Branch voltages and currents. Electric power. Independent voltages and currents in a multipole. HOURS: 5
2 Elements of Graph Theory
Generality. Mesh and cuts. Relations between mesh and cuts. Mesh and cuts basis. Matrix formulation. Nodal Matrix. HOURS: 4
3 Voltages and currents branch
Subspaces of voltages and currents. Basis of voltages and currents. Orthogonality between branch currents and voltages vectors. Tellegen's theorem HOURS: 4
4 Constitutive relations
Definitions. Classification of components. Interaction of dipoles with the network topology. HOURS: 5
5 Simple adynamical and time-invariant circuits and bipoles
Adynamical linear components: voltage and current ideal generators, resistor, short circuit, open circuit, nullator and norator. Series and parallel bipoles. Some details on nonlinear bipoles: the ideal diode. Series and parallel connection of nonlinear bipoles. HOURS: 5
6 Adynamical, linear and time-invariant two-ports
Implicit and explicit representations. of the two-ports properties. Controlled sources, ideal transformer, gyrator and operational amplifier (nullor). Resistive tripoles, delta and star connections and their equivalence. Resistive bridges. Connection in series, parallel, and cascade of two-ports. Examples of operational amplifier circuits, transformers and gyrators HOURS: 10
7 Properties and theorems of adynamical time-invariant and linear circuits
Method of Nodal Tableau. Pathological circuits. Theorem of relocation of independent sources. Theorem of superposition. Theorems of Thevenin and Norton. Millmann theorems. substitution theorem. HOURS: 10
8 Analysis methods for adynamical time-invariant and linear circuits
Nodal method. modified nodal method. Method of meshes and rings. practical methods for the analysis. Examples. HOURS: 5
9 Dynamical linear circuits and bipoles
Capacitors and inductors. Energy and state. Dynamic equations of elementary circuits. Coupled inductors, and their models. ORE: 5
10 Dynamical linear circuits transient behaviour
The order of complexity of a network and its determination. Transients in the first order circuits. Transient and permanent response. Convolution integral and its meaning. Transients in the second-order circuits. HOURS: 7
11 Electrical circuits in sinusoidal regime
Method of Phasors (Steimetz). Network functions in sinusoidal regime. Power in sinusoidal regime. active, reactive and complex power in bipoles and two.ports. multifrequency regime. Maximum power transfer theorem. Resonant circuits. HOURS: 7 Didactic methods
- The course is organized as follows:
- lectures on all subjects of the course;
- classroom exercises related to the theoretical arguments entitling finding the solution of circuits with increasing complexity;
- laboratory experiments (where students are divided in groups) having as subject the measurement of the characteristics of a two-ports and the measurement of the transient behavior in an RC circuit. Learning assessment procedures
- Passing the final exam is the proof that knowledge and abilities outlined in the training objectives of the course have been achieved.
The final examination is a written test about solutions of circuits. Three exercises will be proposed to the student of the most important topics of the course ( operation amplifiers, transient, dc circuits and ac circuits analisys).
Time allowed is 2h 30, any reference text can be used by the student during the test (open-book exam) Reference texts
- Notes by Prof. Amedeo Premoli, Polytechnic of Milan which can be downloaded in the web-site of the course;
Charles K. Alexander, Matthew N.O. Sadiku,"Fondamenti di Circuiti Elettrici", Mc Graw Hill, 2001;
For a deeper level of presentation of the material, some arguments can also be found on:
L. O. Chua, C. A. Desoer, E. S. Kuh, "Linear and Nonlinear Circuits", Mc Graw Hill, 1987
