- Teaching
- MANAGEMENT ENGINEERING
- ELECTRICAL CIRCUIT THEORY

## ELECTRICAL CIRCUIT THEORY

## Teaching schedule

### Language

Italian

### Course description

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

At the end of the course, the student has to demonstrate to know and understand the issues related with circuit model, steady-state analysis of linear circuits and transient analysis of linear circuits.

Applying knowledge and understanding

At the end of the course, the student has to demonstrate 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.

Making judgements

The student must be able:

- to understand a problem and to build the logical path leading to its solution.

- Determine the most appropriate and effective method for the analysis of linear circuits.

Communication skills

The student must be capable to express technical arguments in a clear way, and

capable to perform clear oral or written explanation of selected topics of the course.

Learning skills

The student must be able to perform consultation of bibliographical material,

to integrate knowledge from different sources in order to obtain deeper understanding of the topics of interest,

to develop, outline and summarize the acquired knowledge.

### Prerequisites

The course requires basic mathematical and physical knowledge from the courses of linear algebra, mathematical analysis and general physics:

- 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, differential operators and vector fields);

- elements of general physics (forces, work, energy).

### Syllabus

- 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.

- 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.

### Teaching Methods

Frontal lectures; classroom exercises.

### Textbooks

Textbook in Italian:

M. de Magistris, G. Miano, Circuiti: fondamenti di circuiti per l’Ingegneria, Springer 2007.

Textbook in English:

J. W. Nilsson, S. A. Riedel, Electric circuits 9th edition, Prentice Hall (2010).

### Learning assessment

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):

A: 30-27

B: 26-22

C: 21-18.

- 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 is determined as an average between the results of the written and oral examinations and is expressed in thirtieths.

### More information

Additional didactic material is available on the e-learning platform of the Engineering Department, at the URL http://edi.uniparthenope.it. Access to the platform occurs through authentication with student credentials.