B5603 - SISTEMI E CIRCUITI ELETTRICI LINEARI

Learning outcomes

The analysis of linear systems is a fundamental tool in the education of an engineer. It is a discipline that connects foundational knowledge in mathematics, algebra, and geometry with core subjects in electronics and telecommunications. At the end of the course, the student will have acquired the skills necessary for the analysis of linear systems, with particular focus on linear electrical networks in dynamic conditions.

Course contents

• From electromagnetic theory to circuit theory: definition of electrical circuit, quasi-static electromagnetism, voltage and current, electrical components and constitutive laws, dipoles, n-poles, n-ports, Kirchhoff’s laws, reference directions and conventions.
• Static components: resistor, independent voltage source, independent current source. Series and parallel of resistors.
• Solution of a static linear circuit: general Kirchhoff method, node-voltage method.
• Theorems of linear electrical networks: superposition principle, Thevenin’s theorem, Norton’s theorem, Millman’s theorem, maximum power transfer theorem.
• Linear static two-port networks: resistive two-port networks, resistance and conductance matrices, hybrid matrices, transmission matrices, series and parallel of resistive two-port networks.
• Linear dynamic circuits: memory components, linear inductor, linear capacitor, state variables and initial state, time-continuity postulate of energy. First- and second-order dynamic circuits, solution of the circuit with time-constant excitation, homogeneous solution and particular solution, time constants, transient and steady-state components of the solution.
• Circuits under alternating current steady-state: sinusoidal quantities, Steinmetz transform and inverse transform, phasors, symbolic method, symbolic Kirchhoff’s laws, symbolic Ohm’s law, impedance and admittance. Solution of circuits under sinusoidal steady-state. Power in sinusoidal steady-state, instantaneous power, active power, reactive power, complex power. Thevenin and Norton theorems in sinusoidal steady-state. Two-port networks in sinusoidal steady-state, impedance matrix, admittance matrix, hybrid and transmission matrices.
• Linear dynamic circuits and dynamic systems: algebraic-differential system, state equation and output equation, eigenvalues and time constants, stability and asymptotic stability. Solution of first-order linear state equation, characteristic equation and time constant, free and forced response. Stability of first-order systems. Second-order state equation general solution, real and distinct eigenvalues, real and repeated eigenvalues, complex conjugate eigenvalues. Stability of second-order systems. Generalization to n-th order systems.
• Frequency analysis: transfer function, Bode diagrams, resonance and anti-resonance, first-order passive filters, low-pass and high-pass filter, second-order passive filters, band-pass and band-stop filter.
• Introduction to the Laplace transform applied to the study of dynamic circuits: Laplace transform and inverse transform, fundamental properties, electrical components in the Laplace domain, impedance and initial state, solution of circuits in the Laplace domain, transfer function, poles of the transfer function and eigenvalues of the dynamic system.
  

Readings/Bibliography

Reference texts:

• C. Alexander, M. Sadiku, "Fundamentals of Electric Circuits", McGraw-Hill
• A. Hambley, “Electrical Engineering Principles and Applications”, Pearson

Teaching methods

The course consists of 60 hours of teaching. 40 hours are dedicated to theory and 20 to exercises.

Assessment methods

The exam is subdivided in two parts: exercises and theory. In order to access the theory test, a minimum grade of 18/30 must be obtained in the exercises test.

Exercises

• Two exercises based on the topics covered during the lectures. The duration of the exam is two hours. Required material: calculator. Optional material: one handwritten A4 formula sheet (double-sided).

Theory

• The theoretical part consists of two open questions on the theoretical topics covered during the lectures. The duration of the exam is one hour. Required material: calculator.

The final grade is given by the average of the two tests. See the Virtuale course page for further details.

Teaching tools

Lectures are delivered using a virtual whiteboard and/or video projector. Handwritten notes and any slides shown during the course will be made available.

Office hours

See the website of Arturo Popoli