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    7. Basic Circuits

    Basic Circuits

    CFU: 9

    Prerequisites

    -

    Preliminary Courses

    Analisi Matematica II, Fisica Generale II.

    Learning Goals 

    The aim of this course is to provide students with the basic notions of the theory of circuits in stationary, sinusoidal and periodic steady-state and of linear dynamic circuits of the first and second order; to systematically introduce the general properties of the circuit model, the main theorems, and the main methods of analysis.

    Expected Learning Outcomes 

    Knowledge and understanding

    This course provides students with the knowledge and basic methodological tools necessary to analyze linear circuits, in stationary, sinusoidal and periodic steady-state, and to analyze linear dynamic circuits of the first and second order. The student will be able to recognize the limits of validity and the main implications of the basic theorems of circuits.

    Applying knowledge and understanding

    The student needs to show the ability to solve linear circuits, in stationary, sinusoidal, and periodic steady-state operation; to solve linear dynamic circuits of the first and second order; to identify the most appropriate solution method; and to use where necessary the main circuit theorems. The student needs to show to master the basic concepts of circuit theory and to derive the main theorems correctly using the jargon.

    Course Content - Syllabus

    1. THE LAWS OF ELECTROMAGNETISM

    Electric charge, electric current, current density. Electric field, magnetic field, Lorentz force. The laws of electromagnetism in vacuum in integral form. Law of charge conservation. {The laws of electromagnetism in matter in integral form}. Work of the electric field, energy stored in the electric field, energy stored in the magnetic field, electric power, electric energy. Units of measure.

    1. THE CIRCUIT MODEL

    Electric circuits in slowly changing conditions. Two-terminal element: intensity of electric current, electric voltage, electric power, electric energy. Reference Directions. Passive/active sign convention. Kirchhoff's laws. Canonical two-terminal elements: resistor, switch, independent generators, capacitor, inductor. Real generators. Active, passive, dissipative, and conservative Two-terminal element. {Frequency limits of the circuit model.}

    1. CIRCUIT EQUATIONS

    Simple resistive circuit; non-linear resistive circuit and graphical solution method; {Newton Raphson's algorithm}; linear dynamic circuits of the first order, stationary and sinusoidal steady state. Circuit graph, digraph, subgraph. Connected graph, loop, tree, co-tree, {cut set}; planar graphs and rings; fundamental loop set {and fundamental cut set}; incidence matrix and reduced incidence matrix, {loop matrix and reduced loop matrix}, Kirchhoff equations in matrix form, independent Kirchhoff’s voltage equations, independent Kirchhoff’s current equations, the system of fundamental equations. Node analysis; {mesh current analysis}. Tableau analysis. Conservation of virtual powers (Tellegen's theorem); conservation of electrical powers.

    1. GENERAL RESISTIVE CIRCUITS

    Equivalent transformation of electric circuits, series and parallel connections of resistors; voltage and current divider rules, series and parallel of ideal generators and pathological cases, equivalence transformation of real generators; linear resistive circuits, superimposition principle; equivalent Thevénin-Norton generator; No-voltage gain property {No-current gain property}. Y-Δ transform.

    1. MULTI-TERMINAL AND MULTI-PORTS CIRCUIT ELEMENTS

    N-poles, descriptive currents, and voltages. Two-ports: absorbed electrical power; linear controlled voltage and current sources, ideal transformer; gyrator. Resistive two-ports, reciprocity theorem, resistance matrix, conductance matrix, {hybrid matrices, transmission matrix} mutually coupled circuits (transformer), characteristic relations, perfect coupling, equivalent circuits. {Interconnections of two-ports}. Synthesis of two-ports: T and π configurations.

    1. CIRCUITS IN STEADY-STATE

    Steady-state analysis. Sinusoidal steady-state analysis. Phasors, symbolic method; complex numbers. Impedance, impedance circuits, properties of impedance circuits. Instantaneous power, complex power, average power, reactive power. Phasor diagrams of elementary two-terminal elements. Conservation of complex power, average power and reactive power. Impedance two-terminal elements; analysis in periodic regime. Averaged power due to several sinusoidal inputs. Resonant circuit, quality factor, power and energy balances, {universal resonance curves}. Frequency response of a circuit; filters. {Three-phase systems, star center displacement and Millman formula, power measurement and Aron insertion.}

    1. LINEAR DYNAMIC CIRCUITS

    State equations and state variables of first order circuits, State equations and state variables of second order circuits, associated resistive circuit. Continuity of state variables; solution of first and second order circuits. Free evolution, forced evolution, natural modes of evolution, natural frequency, time constant, transient term, permanent term, dissipative circuit, time-varying circuit, {circuit with impulsive forcing}; solution of second order circuits: series RLC circuit, parallel RLC circuit, natural aperiodic modes, natural oscillating modes, second-order RC and RL circuits. {Impulse response and convolution integral, operating impedances, network function and analysis in the Laplace domain. Introduction to electric circuit simulation and the use of SPICE.}

    N.B. The choice among the arguments enclosed in {curly brackets} may vary according to the choices of the teachers of each channel.

    Readings/Bibliography

    Main Textbook

    1. de Magistris, G. Miano, Circuiti, II edizione, SPRINGER, settembre 2009.

    Additional Textbook

    • O. Chua, C.A. Desoer, E.S. Kuh, Circuiti Lineari E Non Lineari, Jackson, 1991.
    • Miano, Lezioni Di Elettrotecnica, Ed. Cuen, 1998;
    • De Menna, Elettrotecnica, Ed. Pironti, Napoli, 1998.
    • D. Mayergoyz, W. Lawson, Elementi Di Teoria Dei Circuiti, Utet, 2000.
    • A. Haus, J.R. Melcher, “Electromagnetic Fields And Energy,” Prentice Hall, 1989

    Exercises

    • Bobbio, L. De Menna, G. Miano, L. Verolino, Quaderno N ° 1: Circuiti In Regime Stazionario, Ed. Cuen, Napoli, 1998.
    • “ ” Quaderno N ° 2: Circuiti In Regime Sinusoidale, Ed. Cuen, Napoli, 1998.
    • “ “ Quaderno N ° 3: Circuiti In Evoluzione Dinamica: Analisi Nel Dominio Del Tempo Ed. Cuen, Napoli, 1998.
    • Bobbio, Esercizi Di Elettrotecnica, Ed. Cuen, Napoli, 1995.    

    Mooc

    Mooc available on https://www.federica.eu/

    Teaching Methods

    Lectures for approx. 60% of total hours; practical exercises for approx. 40 % of total hours.

    Examination/Evaluation criteria

    Exam type

    Written and oral. Questions of the written exam refer to: numerical exercises.