Linear Networks Analysis and Synthesis

Linear networks analysis and synthesis (214 - 13331)
Study: Bachelor in Audiovisual System Engineering
Semester 2/Spring Semester
2nd Year Course/Lower Division

Students are Expected to have completed:
Linear Algebra
Systems and Circuits
Linear Systems

Compentences and Skills that will be Acquired and Learning Results:

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 mesh and node copedance matrices y 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.

Description of Contents: Course Description

Unit 1: Systematic Linear Network analysis in stationary sinusoidal regimes with mesh and nodal analysis.(PO a, PO e, PO g, PO k)
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
Unit 2: Linear Network analysis using the unilateral Laplace transform (PO a, PO e, PO g, PO k)
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. Networks with mutual inductance and transformers
2.4. Transfer functions. Frequency response. Phase and amplitude response.
Unit 3: Two-port network analysis (PO a, PO e, PO g, PO k)
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. (PO a, PO c, PO e, PO g, PO k)
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 (PO a, PO c, PO e, PO g, PO k).
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. Approximation theory for FIR filters. Windowing.
5.4. 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 (2.57 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 (2.57 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.

CONTINUAL/FINAL AND EVALUATIVE ASSESSMENT (0.86 ECTS)
They will be held a week past the end of each unit (whenever possible depending upon calendar constraints). Their content will be related to the most important concepts in the last unit. This type of assessment is intended both to provide a continual evaluation scheme, thus it contributes to final assessment, and an evaluative scheme: the aggregate, anonymised results of the assessment tests will be reviewed in class to highlight strong and weak points in the student population for that test (see below).
As part of the continuous assessment activities there will be a total of three lab sessions during the course.
These lab sessions may be done in pairs and consist of some previous work that the student must complete before attending the laboratory.
For this purpose, students will be provided with a script including the activities / exercises to be performed, normally in the form of a theoretical analysis for a proposed circuit. The laboratory activities will be typically aimed at comparing the theoretical results previously obtained outside the laboratory with those obtained by either the use of simulation tools or taking measurements from any hardware setup.

TUTORING
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:

Final assessment will comprise a weighted aggregate of evaluative assessment and final evaluation test. Weights are to be found above. A minimum grade of 4 out of 10 in the final exam will be required to pass.

The final evaluation test will comprise both theoretical questions and problems resembling those of the formative evaluation tests, about all the units in the subject.

Basic Bibliography:

Alan V. Oppenheim, R. W. Shafer and J. R. Buck. Discrete-time signal processing. Prentice Hall. 1999
G. C. Temes, J. W. Lapatra. Introduction to Circuit Synthesis and Design. New York, NY, McGraw-Hill, 1977.
J.W. Nilsson. Circuitos Eléctricos (6ª ed., 2001). Prentice Hall.

Additional Bibliography:

A. Papoulis. Circuits and Systems: A Modern Approach. Holt, Rinehart & Winston, 1980.
F. J. Taylor. Principles of Signal and System. McGraw-Hill, 1994.
P. R. Adby. Applied Circuit Theory. Matrix and Computer Methods. Ellis Horwood Series: Electrical and Electronic Engineering, John Wiley & Sons, 1990.
R. Decarlo, P. M. Lin. Circuit Analysis, vol. 2. Prentice-Hall, 1995.
S. Karni. Applied Circuit Analysis. John Wiley & Sons, 1988..
W. M. Siebert. Circuits, Signals and Systems. MIT Press, 1985.