COURSE LANGUAGE: English

YEAR OF THE DEGREE PROGRAMME (I, II, III): II

SEMESTER (I, II, ANNUAL): II

CFU: 9

REQUIRED PRELIMINARY COURSES (IF MENTIONED IN THE COURSE STRUCTURE “REGOLAMENTO”) 
Calculus I, Physics I, Geometry and Linear Algebra.

PREREQUISITES (IF APPLICABLE) 
Calculus II, Physics II.

LEARNING GOALS 
Students will gain a solid foundation of electromagnetism in steady-state and quasi-static regimes and a rigorous foundation in circuit theory. They will be able to analyze stationary, sinusoidal, and periodic steady-state circuits; model and solve linear first- and second-order dynamic circuits; and connect circuit-level descriptions to underlying electromagnetic field models within their domains of validity.

EXPECTED LEARNING OUTCOMES (DUBLIN DESCRIPTORS) 

Knowledge and understanding 
Upon completion of this course, students will have a grasp of electromagnetism in steady-state and quasi-static regimes and the methodological tools required to analyze linear circuits. They will be able to treat stationary, sinusoidal, and periodic steady-state operation, and to model and solve linear first- and second-order dynamic circuits. They will also understand the domains of validity of these models and the principal implications of the fundamental circuit theorems. 

Applying knowledge and understanding 
By the end of the course, students will demonstrate the ability to effectively apply their knowledge and understanding of circuit theory. They will exhibit proficiency in deriving the circuit model from EM fields in quasistatic condition and of solving linear circuits operating in stationary, sinusoidal, and periodic steady-state conditions, as well as linear dynamic circuits of the first and second order. Students will showcase their capability to identify the most appropriate solution methods for different circuit scenarios and effectively utilize the core circuit theorems when necessary.

COURSE CONTENT/SYLLABUS 

• REVIEW 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. 
• 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. Derivation of characteristic equations from field in quasistatic conditions. Frequency limits of the circuit model. 
• 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. 
• 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. 
• 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, {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.   
• 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. 
• 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; solution of second order circuits: series RLC circuit, parallel RLC circuit, natural aperiodic modes, natural oscillating modes, second-order RC and RL circuits. {Brief introduction to a circuit’s impulse response and Laplace-domain analysis.} 
• FROM FIELDS TO CIRCUITS
  Electroquasi-static model. Magnetoquasistatic model. Quasistatic conduction (current-field) model. Assumptions and limits of validity. Derivation of lumped-element constitutive relations from the quasistatic models. Frequency limits of the circuit model. Partial capacitances and capacitor networks. Magnetic circuits; behavior of ferromagnetic materials; Hopkinson’s laws. 

  N.B. Topics enclosed in {curly brackets} are optional. 

READINGS/BIBLIOGRAPHY 

Principal Textbook 
[PT1] L. O. Chua, C. A. Desoer, E. S. Kuh, Linear and Nonlinear Circuits (McGraw-Hill, New York, 1987). 

[PT2] M. De Magistris, G. Miano, Circuiti, 2ª ed. (Springer, Milano, 2009). 

[PT3] A. Haus, J. R. Melcher, Electromagnetic Fields and Energy (Prentice Hall, Englewood Cliffs, 1989). Note: an open-access version is available via MIT OpenCourseWare. 

Additional Textbook 
[AT1] L. De Menna, Elettrotecnica (Pironti, Napoli, 1998). 

[AT2] G. Miano, Lezioni di Elettrotecnica (CUEN, Napoli, 1998). 

[AT3] I. D. Mayergoyz, W. Lawson, Basic Electric Circuit Theory: A One-Semester Text (Academic Press, San Diego, 1998). 

Massive Open Online Course (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.

In case of a written exam, questions refer to:

• Numerical exercises.