Course: 2023/2024

Linear networks analysis and synthesis

(15377)

Requirements (Subjects that are assumed to be known)

Linear Algebra (1º)
Systems and Circuits (1º)
Linear Systems (2º)

1. Transversal/Generic learning outcomes (Be capable of...)
- solving mathematical analysis and synthesis problems.
- apply scientific and technical knowledge to practical situations.
- solve problems stated mathematically.
- integrate theoretical knowledge into the solution of problems.
2. Specific learning outcomes
* Cognitive (be capable of stating...)
- deciding and stating the advantages of using mesh or node analysis for a particular network.
- identifying matrices of mesh and node methods and tell whether they belong to reciprocal systems.
- naming and identifying the different types of system functions/transfer functions for stable causal linear networks and the relationships between responses in the Laplace, real frequency and time domains.
- describing part of a network as a two-port.
- name the different types and manifestations of power in a network with two-ports.
- stating the maximal power transfer theorems for generators and loads with and without an interposing two-port.
- state the concept of conjugate matching.
- relating natural and logarithmic power units.
- stating the conditions for a network to be reciprocal and/or symmetrical
- describing the filter synthesis process.
- graphing the analog filter prescription functions in modulus and attenuation.
- stating the difficulties in synthesising an ideal low-pass transfer function.
- stating Approximation Theory for the design of low-pass LC analog filters.
- mathematically describing frequency transforms for high-pass, band-pass and suppressed-band filters.
- state the advantages of working in normalized frequency, impedance, resistance, inductance and capacitance.
- differentially characterizing, wrt the analog version, the transfer function in the Z domain of digital filters both for infinite and finite impulse responses (IIR & FIR)
- stating a discrete-time domain response from a difference equation.
- sketching direct architectures for digital filters.
* Procedural/instrumental (e.g. Be capable of working out...)
- stating and solving analysis equations for linear networks with mesh and node methods both in stationary sinusoidal and in stationary and transient regimes with the unilateral Laplace transform.
- same with two-ports included in them.
- describing two-ports by their impedance, admittance, power transfer and image parameters.
- specifying and synthesising passive low-, high-, bandpass and suppressed band analog filters using the Butterworth and Chebychev approximations.
- specifying and synthesising said filters in the digital case resorting to analog sinthesis.
- simulating analog filters digitally.

Skills and learning outcomes

Description of contents: programme

Unit 1: Systematic Linear Network analysis in stationary sinusoidal regimes with mesh and nodal analysis.
1.1. Description of RLC components in SSR.
1.2. Using systematic methods for linear network analysis
1.2.1. Mesh analysis
1.2.2. Nodal analysis
1.3. Networks with mutual inductance and transformers
1.4. Real, reactive, and apparent powers. Complex conjugate matching.
Unit 2: Linear Network analysis using the unilateral Laplace transform.
2.1. The unilateral Laplace transform
2.2. The generalisation of analysis theorems to the Laplace domain. Use in network analysis: free, driven, stationary and transient regimes.
2.3. Transfer functions. Frequency response. Phase and amplitude response.
Unit 3: Two-port network analysis
3.1. Two-port description: [z], [y] and [F] parameters.
3.2. Two-port interconnection.
3.3. Image parameters.
3.4. Loaded two-ports. Insertion and transmission losses. Matched two-ports. Conjugate matching. Logarithmic measurement units: Nepers and decibels.
Unit 4: An introduction to the synthesis of passive, analog filters.
4.1. Filtering. Phase and group delay. Phase equalisation. Filter types. Filter specification.
4.2. Filter characterization functions.
4.3. Low-pass filter approximation theory. Parameter normalization. Frequency transformations.
4.4. Butterworth and Chebychev filter synthesis: low-pass, high-pass, band-pass and suppressed band.
Unit 5: An introduction to the synthesis of digital filters.
5.1. A comparison with analog filters.
5.2. Z domain transfer functions with infinite and finite impulse responses. Difference equations. Direct architectures. Stability.
5.2. FIR filter synthesis from analog synthesis.
5.3. Analog filter simulation with digital filters.

Learning activities and methodology

Four different teaching/learning activities will be used: theoretical lectures, problem-solving sessions, problem solving assignment and formative evaluation assessment tests.
ECTS credits include in all cases an allotment for personal work and team problem-solving work.
Theoretical Lectures (2,48 ECTS)
Theoretical lectures will include the use of blackboard and slide material to illustrate main concepts in subject. The explanation of theoretical concepts will be complemented with exercises and problem solution sketches. These lectures will require personal initiative and research plus theoretical study: he/she might be asked to develop particular concepts or apply them to specific problem instances either individually or in group.
PROBLEM SOLVING-SESSIONS AND PROBLEM-SOLVING ASSIGNMENTS(2,64 ECTS)
For problem-solving sessions, students will be given problem statements in advance. Sometimes they will be required to meet in or off class time with fellow students to made solution easier. Problem solving will include common review of solutions and instructor-led correction. These should help ground knoledge and develop the ability to analyse and transmit information relevant to problem-solving. Common review is expected to improve opinion exchange between instructors and students.
Each one of these sessions could inclue a shoft continuous assessment test about the topics studied during the week.
PRACTICAL EXERCISES (0,86 ECTS)
Two practcical exercises will be held a week past the end of units 2 and 4. CAD software tools will be used to simulate the behaviour of circuits whose analysis and synthesis have been studied in the previuous weeks. The student will be able to apply the studied topics to a simple engineering problem.
Individual tutoring sessions are intended to involve specific, clearly defined aspects. Appointments will be managed through the learning management system being used during the course. Collective tutoring sessions will be held after evaluative assessment sessions and their marks are made public to provide feedback to the group about the solution and assessment results.

Assessment System

- % end-of-term-examination 60
- % of continuous assessment (assigments, laboratory, practicals...) 40

Calendar of Continuous assessment

Basic Bibliography

- A.V. Oppenheim and R.W. Shafer. Discrete-Time Signal Procesing. Prentice-Hall: Englewood Cliffs NJ. 1989
- Anant Agarwal. Foundations of Analog and Digital Electronic Circuits. Elsevier. 2005
- C. K. Tse. Linear circuit analysis. Addison-Wesley. 1998
- G.C. Temes and J.W. Lapatra. Introduction to Circuit Synthesis and Design. McGraw-Hill: NY. 1977
- J.W. Nilsson and S. Riedel. Eletric Circuits. Addison Wesley: Reading MA. 1992
- R. A. DeCarlo. Linear Circuit Analysis. Oxford University Press. 2001
- Santiago Cogollos Borrás. Fundamentos de la teoría de filtros. Universitat Politécnica de Valéncia. 2016

- Paul Falstad, Ian Sharp · Falstad circuit simulator : https://www.falstad.com/circuit/

Additional Bibliography

- A. Papoulis. Circuits and Systems. A modern Approach. Holt, Rinehart & Winston: New York NY. 1980
- F.J. Taylor. Principles of Signal and System. McGraw-Hill: New York NY. 1994
- P.R. Adby. Applied Circuit Theory Matrix and Computer Methods: Ellis Horwood Series on Electrical and Electronic Engineering. John Wiley & Sons. 1990
- R. Decarlo and P.M. Lin. Linear Circuit Analysis Vol. II. Prentice-Hall: Englewood Cliffs NJ. 1995
- S. Karni. Applied Circuit Analysis. John Wiley & Sons: New York NY. 1988
- W. M. Siebert. Circuits, Signals, and Systems. MIT Press: ISBN: 0262192292. 1985

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The course syllabus may change due academic events or other reasons.