ELECTRICAL CIRCUIT THEORY
The objective of the course is the definition of the circuit model and the analysis of its fundamental properties. Furthermore, the development of methods for the solution of electrical circuits is addressed.
Learning results (according to Dublin descriptors)
Knowledge and understanding
- Knowledge of the circuit model
- Steady-state analysis of linear circuits.
- Transient analysis of linear circuits.
Applying knowledge and understanding
- Capability to analyze and solve DC/AC steady-state linear circuits.
- Capability to analyze and solve the transient dynamics of generic first and second-order linear circuits.
- Determination of the most appropriate and effective method for the analysis of linear circuits.
- Capability to perform oral or written explanation of selected topics of the course.
- Ability to search for tools and opportunities to improve the knowledge
- Ability to develop, outline and summarize the acquired knowledge
The course requires basic mathematical and physical knowledge. In particular, elements of linear algebra (matrices, determinants, systems of linear equations), elements of complex numbers algebra, elements of mathematical analysis (differential and integral calculus, linear differential equations with constant coefficients), elements of general physics (forces, work, energy).
- The circuit model (10 hours lectures + 2 hours exercises)
Fundamental physical quantities: charge, current, voltage. Ideal one-port circuit elements, voltage and current. Kirchhoff’s laws. Energy aspects for electrical circuits: absorbed power, energy. Fundamental one-port elements, active, passive, dissipative, conservative one-port elements.
- Analysis of simple circuits (6 hours lectures)
Linear and nonlinear resistive circuit, graphical method os solution, Newton-Raphson algorithm; simple first-order linear dynamical RC and RL circuits, transient and steady-state regime.
- Linear resistive circuits (6 hours lectures + 6 hours exercieses)
Equivalence between two one-ports. Series and parallel equivalence, superposition principle, Thevénin-Norton’s theorem. Delta-Wye equivalence and transformations.
- General circuit properties (6 hours lectures)
Circuit graphs: nodes, loops, tree, co-tree. Incidence matrix, loop matrix, Kirchhoff’s Laws in matrix form, linearly independent Kirchhoff’s equations. Fundamental circuit equation system, nodal and mesh current analysis. Electrical power conservation and Tellegen’s theorem. Non-amplification of voltages and currents.
- Linear dynamical circuits in DC/AC steady-state (10 hours lectures + 6 hours exercises)
Linear circuits in sinusoidal steady-state, phasors, symbolic method, impedance circuits and properties; complex power, average power, reactive power and conservation properties; general impedance two-ports and resonance; linear circuit in periodic and quasi-periodic steady-state. Frequency response of a linear dynamical circuit: low-pass, high-pass, band-pass, band-stop filters. Basic aspects of electrical power transmission: high voltage transmission and power factor correction. Symmetric three-phase circuits: balanced, unbalanced.
- Multiterminal circuit elements (6 hours lectures + 4 hours exercises)
Circuit elements with N terminals, two-ports elements, linear controlled sources, gyrator, ideal transformer; resistive two-ports, characterization of linear two-ports, mutually coupled circuits, transformer.
- Linear Dynamical circuits (8 hours lectures + 2 hours exercises)
Dynamical circuits: state equations, associated resistive circuit, continuity of state variables, solution of first-order circuits, zero-input response, zero-state (forced) response, natural modes, natural frequencies, time constant, transient solution, permanent steady-state solution, dissipative circuits, time-variant circuits, solution of RLC series and parallel circuit, aperiodic and oscillating natural modes, general analysis of RC, RL, RLC second-order circuits. General methods of solution for linear time-invariant dynamical circuits.
M. de Magistris, G. Miano, Circuiti: fondamenti di circuiti per l’Ingegneria, Springer 2007.
The purpose of the examination is to check the achievement of the aforementioned skills .
The examination is separated in two stages which take place within a few days:
- written examination (solution of 2 numerical excercises); the written exam has the aim to evaluate the student's ability to solve simple problems by using the methods learned during the lectures and has selective nature (the student who does not exhibit sufficient knowledge of the matter will not be admitted to the oral examination). The duration of the written exam is 2 hours. The use of books, personal computers and smartphones is not allowed, whereas the scientific calculator can be adopted. In order to pass the examination, both excercises must be solved. The result of the written examination is expressed in three ranges, A, B, C, with the following correspondence with grades (in thirtieths):
- Oral examination on all the topics covered in the lectures. The oral exam aims to evaluate the understanding of fundamental topics of the subject and the ability to connect and compare different aspects addressed within the lectures. The final grade takes into account the result of the written examination and is expressed in thirtieths.