eeri 312 pec 2014

SIGNAL THEORY II

STUDY GUIDE FOR

EERI 312 PEC *EERI312PEC*

FACULTY OF ENGINEERING

ii

Study guide compiled by:

Prof WC Venter

Edited nn.

- Page layout by Elsabe Strydom, Graphikos.

Printing arrangements and distribution by Department Logistics (Distribution Centre).

Printed by Nashua Digidoc Centre 018 299 2827

Copyright 2014 edition. Date of revision 2014.

North-West University, Potchefstroom Campus.

No part of this book may be reproduced in any form or by any means without written permission from the publisher.

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MODULE CONTENTS

Welcome and contact information ......................................................................................... iv

Rationale .............................................................................................................................. iv

How to study ......................................................................................................................... iv

Prerequisites .......................................................................................................................... v

Study material ........................................................................................................................ v

Evaluation .............................................................................................................................. v

Action words ......................................................................................................................... vii

Study icons .......................................................................................................................... viii

Warning against plagiarism ................................................................................................... xi

Study unit 1 Network analysis .................................................................................. 1

Study unit 2 Network functions and their realizability ............................................ 3

Study unit 3 Introductory filter concepts ................................................................. 5

Study unit 4 The approximation problem ................................................................ 7

Study unit 5 Sensitivity ............................................................................................. 9

Study unit 6 Basics of active filter synthesis ........................................................ 11

Study unit 7 Positive Feedback Biquad Circuits ................................................... 13

PRACTICALS ............................................................................................................ 15

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160 STUDY HOURS = 16 CREDITS

WELCOME AND CONTACT INFORMATION

Welcome to Signal Theory II. I trust that you will find this module useful during your training as an engineer and that you will enjoy this field of study as an integral part of further studies in engineering.

This module follows Signal Theory I and Linear Systems in which you have learnt the fundamentals of signal theory and electrical and electronic engineering. In this module you will be taught to design passive and active filters for electrical and electronic circuits. You will firstly build on the work you have learnt in Linear Systems by learning how to analyse circuits with active components. You will then study network functions and their realisability, which includes a comprehensive study on the use of the Bode plot in circuit analysis. The rest of the course deals with the design and implementation of passive and active filters in circuits.

You are welcome to contact me during the contact times as indicated on my notice board or to make an appointment with my secretary if you encounter any problems in this module.

Me Engelet van Schoor

School for Electrical and Electronic Engineering

Office: 203

Tel.: 018 299 1903 (w)

[email protected]

RATIONALE

This module elaborates on work you have already studied in Signal Theory I and Linear Systems. It also uses knowledge you have gained in other modules during your first year, such as Mathematics. This subject is a prerequisite for many other subjects in your programme. This is why you need to take on this subject with due respect and do everything in your power to achieve the outcomes successfully. The knowledge you gain now will assist you in the future. What you do not achieve now may be very difficult to catch up with later on.

HOW TO STUDY

Like all engineering subjects, Signal Theory II is not a learning subject and therefore studying it not only involves memorising. Successfully completing the module involves mastering the relevant concepts and techniques. This means that you must work on them yourself and make sure you master the concepts. The only way to achieve this is to prepare for each assigned contact session. This can be done by reading the relevant work and making sure you understand its outcomes. You can tackle the relevant problems and attend the contact sessions with possible solutions at hand. It also helps to discuss problems in a group context, because it is good to learn from each other and from each other’s mistakes.

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We do, however, recommend that you do the textbook exercises on your own. Although most of the exercises will be dealt with during class and tutorials, you have to work through all exercises on your own to ensure your understanding of the work and the correctness of your own answers. Please work through all the problems at the end of each chapter to obtain the correct answers. The answers are available at the end of each chapter or from me. This ensures that you will not encounter problems during class tests, semester tests or examinations.

A student of average intelligence, who diligently perserveres and shows a keen interest in a module such as this, will succeed! However, successful studies will be compromised if you have no motivation or show no interest in the subject – no matter how gifted you are.

Our advice is therefore: Put everything you have into this module and build a sound foundation of knowledge which will inspire you to such an extent that nothing will stop you from succeeding. My best wishes accompany you for the rest of your studies.

PREREQUISITES

The prerequisites for this subject are explained in the Yearbook of the Faculty. The required subjects are:

EERI 222 Signal Theory I

EERI 227 Linear Systems

It is also very important for you to have access to a computer equipped with a word processing package wich will enable you to complete your reports. A package that includes spreadsheets on which data reports can be processed will also be handy. Access to the Internet will be a great help as a search engine for further information, although this is not a necessity.

You will need certain hardware to use in practical sessions. Practical sessions also require you to buy certain components. You must, however, obtain information on what you will have to buy for yourself by studying the given prerequisites. (However, these components are not very expensive.)

STUDY MATERIAL

The prescribed textbook for this module is:

Gobind Daryanani, Principles of Active Network Synthesis and Design, John Wiley & Sons, 1976.

In the following, this book will be referred to as “Daryanani”.

EVALUATION

Participation mark and proof of participation

a. Evaluations will be scheduled during the semester in the form of 3 semester tests which will comprise 70% of your semester mark and tutorials making up 15% of the semester mark.

b. Two practical sessions, also scheduled during the semester, will contribute 15% of your participation mark.

c. A participation mark of 40% is required for admission to the examination. All the practical assignments must also be completed and a minimum mark of 50% has to be achieved for them.

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d. Your participation will also be proved by regular attendance at contact sessions and by your contribution during these sessions.

Proof of participation will be issued to you if you comply with these prerequisites. Your proof will serve as admission to the examinations.

Examination mark

You will write one three-hour paper on all the work done during the semester.

A subminimum of 40% is required for the examination.

Final/module mark

The participation and exam mark, carrying equal weights, will make up your final mark.

Calculation of the final mark

Practicals 7.5

Semester tests 35.0

Tutorials 7.5

Exam 50

Final mark 100

You will need a minimum of 50% for your final mark to pass.

A final mark of 75% and higher serves as a distinction.

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ACTION WORDS

Action words are verbs or phrases used to formulate outcomes to achieve assessable and specific learning actions.

Action verb Meaning

Name Give short and factual answers/reasons.

Describe Qualities or facts must be given in a logical and structured way. You are not asked to give your own opinions.

Define A concise though clear description of a term/concept must be given in order to clarify the meaning of it.

Explain Describe a certain process. Every conclusion must be substantiated. Sketches and flow charts/graphs will make your task easier. All sketches and diagrams must, however, be accompanied by a full description to ensure clear meaning.

Compare Do not only define the two relevant issues that have to be compared. A comparison of the two issues, which includes a description of their differences and similarities, is required.

Prove Show whether an allegation is valid or not. A well-structured line of reasoning must be followed, in which you use concrete facts. You must always confirm all your claims.

Deduce Exactly the same is expected here when you have to prove some or other allegation.

Calculate You are required to estimate certain magnitudes. Either numeric or analytical terms will be needed according to the given situation. The calculation process is of great importance. You will have to substantiate certain calculations from time to time. Handle the situation as if you were writing a textbook for a fellow student.

Design This is almost the same as calculate.Typically, you have to calculate (by using a specific method) your components’ value in a specific circuit.

Evaluate If you are required to evaluate a certain situation or situations, you must define your answer. You must also state/name the pros and cons of the situation. Compare situations if more than one situation has to be evaluated. You must take a stand and sustantiate your answer.

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STUDY ICONS

Test your current knowledge/insight.

Individual exercise.

Practical example.

Prepare yourself for participation in the group meeting/contact session on this issue. This is a good example of an examination question.

Take your answers with you to the contact session/group meeting for discussion.

Introductory statements.

Attentively study the following section/ explanation/ discussion..

Study the indicated material in the textbook/article, etc.

Outcomes.

Assignment.

Answers/solutions.

Summary of the main learning points.

Revision.

Approximate study time.

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Module code: EERI312 Prerequisites: EERI222 Signal Theory I,

EERI227 Linear Systems

Module name: Signal Theory II

Module credits: 16 Co-requirements: None

CESM: e.g. 08.19 as registered with ICAS

Module objectives The purpose of the Signal Theory II module is to teach the student to analyze, design and implement active filters.

Module outcomes

At the end of this module the student will be able to analyze active networks, to design active analog filters using different methods and to implement the designs in different ways. The student will know the characteristics of different approximation functions for filter design as well as techniques to practically implement the approximation functions.

Assessment criteria

The following outcomes will be assessed in

this course:

a) The student must be able to analyze

active networks.

b) The student must be able to design

analogue filters using different

approximation functions.

c) The student must be able to implement

approximation functions using

different circuit designs.

Assessment methods and weights

The final course point will be determined as follows:

Practicum Sessions: 7.5%

Tutorials: 7.5%

Semester Tests: 35%

Exam Point: 50%

Total 100%

The class tests, semester tests and exam evaluate the student’s ability to analyze and design analogue filters, as well as the student’s ability to understand the principles on which the designs are based. The practicum sessions evaluates the student’s ability to design, implement and realize active analogue filters

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ECSA Exit Level Outcomes

This module contributes towards the development of the following ECSA ELOs:

Outcome 1: Problem solving.

The student must demonstrate the ability to analyze a problem in its context and break it down

into manageable and solvable components. The outcome is assessed in class tests, semester

tests, practicals and examinations.

Outcome 2: Application of scientific and engineering knowledge. In this course the student must demonstrate competence to apply knowledge of mathematics,

basic science and engineering sciences from first principles to solve engineering problems.

The outcome is assessed in class tests, semester tests, practicals and examinations.

Outcome 3: Engineering Design:

The student is given an engineering problem in the form of a user requirement. The student is

required to assess the information given, formulate the problem and solve the problem

through an appropriate design. The outcome is assessed in class tests, semester tests,

practicals and examinations. In the practical assignment the student must implement the

solution, evaluate the results and report by writing a report.

Detailed content Network analysis by using Laplace transform techniques; analyse network functions for realizability; determine frequency response by using Bode diagram techniques; classify analogue filters in different categories; design analogue filters by using the following approximations: Butterworth, Chebyshev, Elliptic and Bessel; perform frequency transformations on low pass analogue filters; determine the sensitivity of analogue filter transfer functions; analogue filter design and realization by using different approximations.

Knowledge Areas

Mathematics Basic sciences Engineering

sciences

Design and

synthesis

Computers and

IT

Complementary

studies

14 2

Prescribed textbook(s) Daryanani, G. Principles of Active Network Synthesis and Design, John Wiley & Sons.

ISBN: 0-471-19545-6

Module administration

Weeks per semester 14

Duration of lecture period 50min = 0.83 hr

Number of lectures per week 4

Number of tutorials per week 2

Hours of practicals per semester 12

Other contact time per semester (h) 0

Other non-contact time per semester (h)

Total number of hours per semester This is calculated using the ECSA

formula and should approximately

correspond to the credit allocation of the

module

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WARNING AGAINST PLAGIARISM

ASSIGNMENTS ARE INDIVIDUAL TASKS AND NOT GROUP ACTIVITIES. (UNLESS EXPLICITLY INDICATED AS GROUP ACTIVITIES)

Copying of text from other learners or from other sources (for instance the study guide, prescribed material or directly from the internet) is not allowed – only brief quotations are allowed and then only if indicated as such.

You should reformulate existing text and use your own words to explain what you have read. It is not acceptable to retype existing text and just acknowledge the source in a footnote – you should be able to relate the idea or concept, without repeating the original author to the letter.

The aim of the assignments is not the reproduction of existing material, but to ascertain whether you have the ability to integrate existing texts, add your own interpretation and/or critique of the texts and offer a creative solution to existing problems.

Be warned: students who submit copied text will obtain a mark of zero for the assignment and disciplinary steps may be taken by the Faculty and/or University. It is also unacceptable to do somebody else’s work, to lend your work to them or to make your work available to them to copy – be careful and do not make your work available to anyone!

Study unit 1

1

1 NETWORK ANALYSIS

The proposed study time for the study unit 1 is 16 hours.

Study:

Daryanani, Chapter 1 – Parts 1.1 – 1.4.

After completing this study unit, you should be able to

analyse passive RLC circuits on the s-level;

do Thèvenin-Norton transformations on circuits;

deal with dependent circuit sources and dependent stress sources in circuits;

analyse active RLC circuits on the s-level; and

deal with the simple analysis of operational amplifier circuits.

Study unit 1

2

Now do the following problems at the end of Chapter 1 in Daryanani:

1.1

1.2

1.5

1.7

1.17

1.18

The answers are available at the end of the textbook.

Revise the outcomes of this unit in order to make sure that you have achieved them all.

Study unit 2

3

2 NETWORK FUNCTIONS AND

THEIR REALIZABILITY

The proposed study time for Study Unit 2 is 24 hours.

Study:



derive the properties of all network functions;

derive the properties of passive RLC driving point impedances;

derive the properties of passive RC driving point impedances;

derive the properties of passive LC driving point impedances;

derive the properties of transfer functions; and

determine the amplitude and phase plots of network functions.

Study unit 2

4

Do the following problems at the end of chapter 2 in Daryanani:

2.1 a, b and c

2.4

2.5

2.9 a and b

2.14

2.17

2.18

2.32



Study unit 3

5

3 INTRODUCTORY FILTER

CONCEPTS


Study:



not only write down the loss function of a low-pass filter, but also sketch its requirements;

not only write down the loss function of a high-pass filter, but also sketch its requirements;

not only write down the loss function of a band-pass filter, but also sketch its requirements;

not only write down the loss function of a band-reject filter, but also sketch its requirements;

understand and apply gain equalisers;

understand and apply delay equalisers; and

describe the pros, cons and applications of passive, active, electromechanical, digital and microwave filters.

Study unit 3

6


3.1

3.5

3.9 b


Revise the outcomes of this unit in order to make sure that you have achieved them all

.

Study unit 4

7

4 THE APPROXIMATION

PROBLEM


Study:



find the relevant functions by using the Bode plot approximation technique;

find the relevant functions by using the Butterworth approximation technique;

find the relevant functions by using the Chebyshev approximation technique;

find the relevant functions by using the elliptic approximation technique;

find the relevant functions by using the Bessel approximation technique; and

design high-pass filters, band-pass filters and band-reject filters by using frequency transformations.

Study unit 4

8


4.5

4.9

4.17

4.18

4.21

4.24

4.31

4.35

4.36



Study unit 5

9

5 SENSITIVITY


Study:

Daryanani, Chapter 5 – Part 5.1.

After completing this study unit, you should be able to synthesise

elementary driving point functions by means of inspection;

driving point functions by using partial fraction expansion;

driving point functions by using continued fraction expansion;

transfer functions by using singly terminated ladder networks;

transfer functions by using the zero shifting technique; and

transfer functions by using doubly terminated ladder networks.

Study unit 5

10

Do the following problem at the end of chapter 5 in Daryanani:

5.1



Study unit 6

11

6 BASICS OF ACTIVE FILTER

SYNTHESIS


Study:



synthesise the transfer functions by using the cascade approach;

synthesise the transfer functions by using real poles and zeros;

synthesise the transfer functions by using negative feedback topology;

synthesise the transfer functions by using positive feedback topology;

synthesise the transfer functions by using coefficient matching techniques;

adjust the gain constant of synthesised circuits;

apply impedance scaling to synthesised circuits; and

apply frequency scaling to synthesised circuits.

Study unit 6

12


7.1

7.3

7.6

7.7

7.8



Study unit 7

13

7 POSITIVE FEEDBACK BIQUAD

CIRCUITS


Study:



design Sallen and Key low-pass circuits;

design Sallen and Key high-pass circuits;

design Sallen and Key band-pass circuits; and

realise complex zeros by using twin-T networks.

Study unit 7

14

Do the following problems at the end of Chapter 8 in Daryanani:

8.1

8.2

8.3

8.4

8.16

8.17

8.27



Practicals

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PRACTICALS

The practical assignments and list of practical components needed will be provided to you during lectures.

eeri 312 pec 2014

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