Ing Ind - Inf (Mag.)(ord. 270) - MI (471) BIOMEDICAL ENGINEERING - INGEGNERIA BIOMEDICA

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096532 - ADVANCED CIRCUIT THEORY

Ing Ind - Inf (Mag.)(ord. 270) - MI (475) ELECTRICAL ENGINEERING - INGEGNERIA ELETTRICA

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096532 - ADVANCED CIRCUIT THEORY

Ing Ind - Inf (Mag.)(ord. 270) - MI (476) ELECTRONICS ENGINEERING - INGEGNERIA ELETTRONICA

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096532 - ADVANCED CIRCUIT THEORY

Obiettivi dell'insegnamento

Goal of this course TheAdvanced Circuit Theory course is designed tocomplement the basicstudents' knowledgeon electrical circuitsobtained in the courseof the Junior Electrical Engineering degree, with more "in depth" or complementary topics that are typical of a rigourous and scientifical approach to the study of circuits. Inparticular, the analysis oflinear and non-linear circuits, purelyresistive ordynamic is formalised using general methodssuch as modified nodal analysisand state equations. The basic framework of circuit simulators is presented, along with explanations related to possible simulation failures.Finally,network functionsoflineardynamiccircuits are introduced in order to presentsome simple examplesof one-port synthesisandfilter design. Inallthe topics covered, specific attention is given to theapplicationofgeneral methods.

Risultati di apprendimento attesi

Knowledge and understanding (Dublin Descriptor 1)

At the end of the course and after successfully passing the exam, the student:

- knows the fundamental principles of graph theory applied to electrical circuits

- has knowledge of the state space representation of nonlinear dynamic circuits, of the linearisation methods and of energy based stability properties of circuits

- knows how to apply the standard modified nodal analysis method for the solution of general circuits (nonlinear, dynamic etc.) including integration methods and nonlinear solvers.

- Understands the basic properties of linear passive one-ports and knows the standard methods for their realization

- Moreover, as a more general and methodological goal, a rigorous, math based approach to circuits.

Applying knowledge and understanding (Dublin Descriptor 2)

At the end of the course and after successfully passing the exam, the student:

- is able to write solving equations for general circuits and analyzing their solutions both using numerical methods and using closed form solutions

- is able to write, using standard programming languages, the basic structure of a circuit simulator

- knows how to synthesize a passive linear one port using Cauer or Foster methods

Argomenti trattati

1Fundamental lawsof electrical networks

Topological properties. Implicitandexplicit Kirchhoff's laws. Graph matrices and their relations. Power andenergy. Implicit andexplicitConstitutive formulations of one-portandtwo-port components.Unidirectionality, 'reciprocity', symmetryand other propertiesof lineartwo-ports. Special two-ports: transformer, gyratorandoperational amplifiers. Connection oftwo-ports.

Formulationofstate equationsin the time domain. Solutionof thestate equation oflineardynamic circuitsin the time domain: freeand forced components of the solution.Natural frequenciesand stability. Second-orderlinear circuits. Qualitative studyof simpledynamicnonlinear circuits: oscillatorsandbistable. MNA formulation for general circuits. Simple numerical methods for the solution of the MNA problem.

4Network Functions

Analysis of lineardynamic circuits in sinusoidal steady state. Network functions in thephasordomain. Frequency response.Analysis of lineardynamic circuits using the Laplace transform. State equationsandtheirsolutioninthe Laplace domain. Immittances and general network functionsH(s), poles and zeros.

5 Synthesis ofone-ports andpassivefilter design

Properties of immittance functions Z(s) and Y(s) of RLC passive one-ports. Propertiesand synthesis of one-ports withonly two elements(LC, RC, RL) according to the canonical formsofFosterandCauer. Design of alow pass filter.Sensitivity analysiswith respect to aparameterof the circuit andmethodfor that network.

Prerequisiti

Prerequisites All topics that are part of the basic circuit theory course (Elettrotecnica) Laplace transforms Electronic components (diodes, transistors, operational amplifiers, ...) Linearalgebraic equations Eigenvalues andeigenvectorsof matrices Linear time-invariant ordinary differential equations

Modalità di valutazione

The exam is composed of two parts, a first "practical" written test, followed by a second written test related to the theory. The goal of the practical part is assessing the student's capability of application of the main topics of the course with a direct approach to simple problems (Dublin descriptors 1 and 2), the theory part to test the knowledge and understanding of the main methods used in the course aiming at the self-sufficiency in the solution of problems not considered in this course (Dublin descriptor 1).

The date of the practical part is published online on the POLIMI webpage, students can access the theory part either immediately after the practical part (and will be corrected only if the practical part is sufficient), or (in this case only if the practical part is sufficient) after about 7 to 10 days or in any other following exam session (in this case the student will be temporarily marked as non-passed and will have to enroll to the chosen session).

The practical part lasts 2h30' and consists in the solution of three problems covering the main areas of the course, the students must work autonomously but can have access to a single self produced A4 sheet containing formulas or anything else the student believes can be useful to pass this part of the exam. Clarity in the description of the methods used and in the results obtained and terseness of language will be evaluated positively. The practical part is marked from 0/30 to 30/30; access to the theory part is reserved to students with a mark greater or equal to 16/30. The theory part lasts 45' and consists in three questions that must be answered in written form each question taking no more than two A4 pages and where terseness of language and a quantitative approach where possible are encouraged. The theory part, if not sufficient, invalidates the whole exam, if sufficient it can increment or decrement the practical part mark usually in the range -4/+4.

Communication of results, times and places for the theory part will be via mail, using the official POLIMI student mail address.

Bibliografia

Leon O. Chua, Charles A. Desoer, Ernest S. Kuh, Linear and Nonlinear Circuits - International Edition, Editore: McGraw (but now in non defined international reprint), Anno edizione: 1987, ISBN: 9780070108981
Advanced Circuit Theory - Lecture Noteshttps://beep.metid.polimi.it/ Note:

Lecture Notes available on the POLIMI beep platform.

Forme didattiche

Tipo Forma Didattica

Ore di attività svolte in aula

(hh:mm)

Ore di studio autonome

(hh:mm)

Lezione

30:00

45:00

Esercitazione

20:00

30:00

Laboratorio Informatico

0:00

0:00

Laboratorio Sperimentale

0:00

0:00

Laboratorio Di Progetto

0:00

0:00

Totale

50:00

75:00

Informazioni in lingua inglese a supporto dell'internazionalizzazione

Insegnamento erogato in lingua
Inglese

Disponibilità di materiale didattico/slides in lingua inglese

Disponibilità di libri di testo/bibliografia in lingua inglese

Possibilità di sostenere l'esame in lingua inglese

Disponibilità di supporto didattico in lingua inglese