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Students’ Handbook

B.Tech

Electronics and Communication Engineering

Semester-IV

Department of Electronics and Communication

Engineering

Ambala College of Engineering and Applied Research,

Ambala

(Affiliated With)

Kurukshetra University, Kurukshetra

Mission and Vision of the Institute

Vision of the institute

To become a source of technology and start an Incubation Centre for entrepreneurs

resulting in this region developing into a vibrant industrial hub with many startup

companies dealing with new technology.

Mission of the institute

1. To impart quality engineering education to students through quality teaching,

hands on training, and applied research in practical and product oriented projects.

2. To impart such education that passing out students are ready with good theoretical

and practical knowledge to suite the current need of industry.

3. To expose students to applied research, especially the fact that research does not

require much money but does require great persistence.

4. To sow the seed of entrepreneurship in them so that our engineers become job

providers and not job seekers.

5. To train students as a complete person through extracurricular activities and with

an exposure to a transparent system based on ethics so that they believe that a

successful institution and a successful business can be run with ethics without

corruption.

Mission and Vision of the Department

Vision of the Department

Vision of the department is to impart the students of Electronics and Communication

engineering quality teaching embedded with updated and upgraded technical knowledge

based on research and innovations by practical hands on training.

Mission of the Department

1. To make students capable to convert theoretical knowledge into practical knowledge.

2. To frame the students to follow heuristic approach i.e. learning while doing.

3. To impart the knowledge among students to have practical hands on latest software

and technical tools.

4. To inculcate students with hard skills and soft skills.

Programme Educational Objectives

The department has defined its PEOs, which are described as below.

1. To impart to the students knowledge in basic sciences, engineering sciences and

humanities to understand the societal context of engineering.

2. To impart technology based engineering education to students for developing their

analytical skills leading to optimization in system design.

3. To make students capable to be effective in multidisciplinary and diverse professional

environments so that they become capable to work with product based projects

through applied research.

4. To make students capable to function as an individual or as a part of a team,

therefore, enhancing their leadership and cooperative abilities to fulfill the needs of

industry, locally and globally.

5. To develop the desire to keep learning throughout life and a passion towards modern

technical engineering tools for understanding professional and ethical standards.

6. To motivate students to serve and to benefit the society in a constructive manner by

developing soft skills and hard skills in them through training of teachers.

List of Programme Outcomes

1. Knowledge of basic sciences, humanities and engineering.

2. Identify, formulate and analyze to solve complex engineering problems.

3. Capable to design and integrate the systems.

4. Able to work as an individual and in multidisciplinary team.

5. An ability to engage in life-long learning.

6. Ability to communicate effectively.

7. Knowledge of latest design tools.

8. To design and conduct experiments, as well as to analyze and understand data.

9. Understand the impact of engineering solutions in a global, economic,

environmental, and societal context.

10. An ability to use the techniques, skills, and modern engineering tools

necessary for engineering practice.

11. To design a system, component, or process to meet desired needs within realistic

constraints such as economic, environmental, social, political, ethical, health and

safety, manufacturability, and sustainability

Bachelor of Technology (Electronics & Communication, Electronics, Electronics & Instrumentation)

Common for ( ECE, EC, E&I)

Scheme of studies / Examination

(Semester- 4)

Sl.

No.

Course No.

Subject

Teaching

Schedule

Examination Schedule (Marks)

Duration

of Exam

(Hours)

L

T

P

Total

Theory

Sessional

Practical

Total

1

MATH- 201E

/ HUM-201E

Mathematics III /

Basics of Industrial Sociology,

Economics & Management.

3

1

-

4

100

50

-

150

3

2 MAT-204E Computational Techniques 3 1 - 4 100 50 - 150 3

3

ECE-202E

Electronics Instrumentation &

Measurements

3

1

-

4

100

50

-

150

3

4

ECE-204E

Digital Electronics

3

1

-

4

100

50

-

150

3

5

EE-208E

Signals & Systems

3

1

-

4

100

50

-

150

3

6

ECE-206E

Fields & Waves

3

1

-

4

100

50

-

150

3

7

ECE-208E

Electronics Measurements Lab.

- - 3

3

-

50

50

100

3

8

ECE-210E

Digital Electronics Lab.

-

-

3

3

-

50

25

75

3

9

MAT-206E

Computational Techniques Lab.

-

-

3

3

-

50

25

75

3

TOTAL

18

6

9

33

600

450

100

1150

-

ELECTRONICS AND COMMUNICATION ENGINEERING DEPARTMENT

AMBALA COLLEGE OF ENGINEERING AND APPLIED RESEARCH, AMBALA

Subject : Basics of Economics & Management Semester : 4th

Subject Code : HUM-201E Lectures per Week : 3

Theory Marks : 100 Tutorials per Week : 3

Sessional Marks : 50 Practical : -

SYLLABUS

UNIT-I

Meaning of Industrial Economic, production function, its types, least cost combination, law of variable

proportion, law of returns; increasing, constant and Diminishing. Fixed and variable costs in short run and long

run, opportunity costs, relation between AC and MC. U-shaped short run AC curve. Price and output

determination under monopoly in short run and long run, price discrimination, price determination under

discriminating Monopoly, comparison between Monopoly and perfect competition

UNIT-II

Meaning of management, characteristics of management, management Vs administration, management – Art,

Science and Profession, Fayol’s principles of management. Human relations approach. Functions of

management.

UNIT-III

Planning and Organizing: Planning, steps in planning. Planning premises, difference between planning policy

and strategy. Authority and responsibility, centralization and decentralization

UNIT-IV

Staffing, directing and controlling – Manpower planning, Recruitment and section styles of leadership,

communication process and barriers, control process and steps in controlling

Note: Eight questions are to be set in all by the examiner taking two questions from each unit. Students will be

required to attempt five questions in all selecting at least one question from each unit. Each question will be of

equal mark.

TEXT BOOKS:

1. “Modern Economic Theory” Dewett, K.K., S. Chand & Co.

2. “Economic Analysis” K.P. Sundharam & E.N. Sundharam (Sultan Chand & Sons).

3. “Micro Economic Theory” M.L. Jhingan (Konark Publishers Pvt. Ltd.).

4. “Principles of Economics” M.L. Seth(Lakshmi Narain Aggarwal Educational Publishers – Agra).

5. “An Introduction to Sociology”, D.R. Sachdeva & Vidya Bhusan.

6. “Society – An Introductory Analysis”, R.M. Maclver Charles H. Page.

7. “Principles and Practices of Management : R.S. Gupta; B.D. Sharma; N.S. Bhalla; Kalyani.

REFERENCE BOOKS

1. “Organization and Management : R.D. Aggarwal, Tata McGraw Hill.

2. Business Organization and Management : M.C. Shukla.

LECTURE PLAN

LECTURE NO. LECTURE TOPIC

L1 Introduction Industrial economics

L2 Scope of Industrial economics

L3 Production function

L4 Types of production

L5, L6 Law Of Production

L7, L8 Least cost combination

L9 Law of variable proportion

L10, L11 Law of increasing, constant & diminishing returns

L12 Fixed and variable cost in short and long run

L13 Opportunity cost

L14 Relation between Ac &Mc

L15 U-shaped short run PC curve

L16 Price and output determination under monopoly in short and long run

L17 Price Discrimination

L18 Price determination under discriminating monopoly

Tutorial sheet 1

1. What is industrial economics? Explain its scope for engineers and the manager.

2. Discuss the type of production function.

3. Write notes on Laws of Diminishing Returns?

4. What do you mean by opportunity cost?

5. Write the Note on

a. total production

b. Marginal production

c. Average production

6. Relationship between Average cost and marginal cost.

Tutorial sheet 2 1. What is the perfect competition? Explain the feature of perfect competition.

2. What do you understand by Monopoly Market? Explain its features.

3. Price determination under perfect competition.

4. Explain the concept of least cost combination

5. Explain the various types of cost.

6. Explain the various type of monopoly.

Tutorial sheet 3

1. Explain the management with its various features.

2. “Management is both a science and an art” In the light of this statement explain it in Detail.

3. Human relation approach to management.

4. Explain the management as profession

5. Write the note on Management Vs. science

Tutorial sheet 4 1. Explain in brief Henry Fayol’s principle of management.

2. Is the management the part Administration?

3. What are various function of management? Explain it in brief.

4. What do you understand by the importance of management in India

5. Write the note on authority, responsibility and accountability.

Tutorial sheet 5

1. What is planning? Briefly discuss the steps of planning.

L19 Comparisons between monopoly & perfect competition

L20 Management and its characteristics

L21 Management Vs administration

L22 Management is art science & profession.

L23 Henry fayol’s principle of management

L24 Human relation approach

L25 Function of management

L26 Planning & Organizing

L27 Steps in planning

L28 Planning premises

L29 Differences between planning policy &strategy

L30 Authority & Responsibility

L31 Staffing

L32, L33 Directing & controlling

L34, L35 Manpower planning

L36 Recruitment & selection

L37 Styles of leadership

L38 Communication process

L39 Steps in controlling

2. What are the limitations of planning?

3. Describe the important factors to make planning exercise more effective.

4. What do you mean by planning premises? Explain its various types

5. What do you understand by delegation of authority .Explain the principle of delegation of authority

Tutorial sheet 6 1. What do you mean by authority? Define the source of authority.

2. What is the difference between authority and responsibility?

3. Define centralization .Explain the importance of it

4. What is the decentralization? Explain the advantage and

5. Explain the disadvantage of decentralization.

6. Explain the types of strategy.

Tutorial sheet 7 1. Define staffing. Describe various steps in the process of staffing.

2. Define the needs and importance of manpower planning.

3. What are various source of recruitment?

4. What is training? Explain the various type of it.

5. Explain the steps of human resource planning.

6. Write the advantages and disadvantages of internal and external source of Recruitment.

Tutorial sheet 8 1. “Leader is born not made.” Explain the statement.

2. What are the characteristics of good communication system?

3. Define the importance of controlling in business.

4. What are the modern techniques of control?

5. Explain the elements of communication system.

6. Explain barrier to communication system.



Subject : Electronics Instrumentation and Measurements Semester : 4th

Subject Code : ECE-202E Lectures per Week : 3



SYLLABUS

UNIT-I

MEASUREMENT AND ERROR: Functional elements arid generalized configuration of a measuring

Instrument, Characteristics of instruments, errors in measurements and their statistical analysis.

MEASUREMENT OF RESISTANCE: Wheat stone bridge, Carey-Foster Bridge, Kelvin double bridge,

Measurement of Insulation resistance.

UNIT-II

A-C BRIDGES: Maxwell Inductance bridge. Maxwell Inductance Capacitance Bridge, Anderson’s Bridge,

Hay’s Bridge, De-Sauty’s Bridge, Schering’s bridge and Wein’s bridge.

VOLTAGE INDICATING AND RECORDING DEVICES: Analog voltmeters and Potentiometers,

Self balancing potentiometer and X-Y recorders, Galvanometers - Oscillographs, Cathode - Ray Oscilloscopes,

Magnetic Tape Recorders.

UNIT-III:

ELECTRONIC INSTRUMENTS: Wave analyzer, Distortion meter: Q-meter. Measurement of Op-Amp

parameters.

DIGITAL INSTRUMENTS: Digital Indicating Instruments, Comparison with analog type, digital display

methods, digital methods of time and frequency measurements, digital voltmeters.

UNIT-IV

TRANSDUCERS: Classification of Transducers, Strain Gauge, Displacement Transducers -Capacitive

Transducers, LVDT, Piezo-electric Transducers, Temperature Transducers – resistance thermometer,

Thermocouples and Thermistors, Liquid level measurement Low pressure (vacuum) measurement.

DATA ACQUISITION SYSTEMS: A to D and D to A converters, Analog and Digital DataAcquisition

Systems, Multiplexing, Spatial Encoders, Telemetry.

TEXT BOOK:

A Course in Electrical and Electronics Measurements and Instrumentation: A.K. Sawhney; Dhanpat Rai & Sons.

REFERENCE BOOKS:

Electronics Instrumentation and Measurement Techniques: Cooper W.D & Helfrick A.D.; PHI Doeblin E.O.,

Measurement Systems: Application & Design, Mc Graw Hill.

NOTE:

Eight questions are to be set in all by the examiner taking two questions from each unit. Studentswill be required

to attempt five questions in all selecting at least one question from each unit. Each question will be of equal

marks.

LECTURE PLAN

LECTURE

No.

LECTURE TOPIC

L1. Introduction: - Measurements and Error

L2 Fundamental elements arid generalized configuration of a measuring elements

L3 Characteristics of instruments

L4 Error in measurements

L5 Statistical analysis of error

L6 Measurements of resistance

L7 Wheat stone Bridge and Carey-Foster Bridge

L8 Kelvin double Bridge

L9 Measurements of insulation resistance

L10 Revision of 1st unit

L11 A-C bridges: Maxwell Inductance Bridge

L12 Maxwell Inductance Capacitance Bridge

L13 Anderson’s Bridge and Hay’s Bridge

L14 De-sauty’s Bridge

L15 Schering’s Bridge and Wein’s bridge

Tutorial sheet 1 1. What are electronic instruments and its types?

2. Discuss working principle and operation of wave analyzer.

3. Explain the working principle and operation Q meter.

4. What are the measurements of op-amp parameters?

5. An 8 bit D/A converter has Vr = 5 V. what is output voltage when Bin = 10110100? Find also VLSB.

Tutorial sheet 2

1. What are the classifications of Transducers?

2. What is displacement transducer and discuss capacitive transducer.

3. Write short note on LVDT.

4. Explain Piezo-electric transducers.

5. In the circuit given below, the voltage across the resistor of the value 25 KΩ is to be measured first by

using a voltmeter of sensitivity of 20KΩ/V. calculate the reading of voltmeter in each case and the %

error in the measurement.

Tutorial sheet 3

1. Explain resistance thermometer.

2. Write short note on thermocouple.

3. Explain the term thermistors.

4. Define the term liquid level measurement.

5. Calculate the value of the multiplier resistor for a 10 V rms range on the voltmeter shown below

L16 Voltage indicating and record devices : Analog voltmeters and potentiometer

L17 Self balancing potentiometer and X-Y recorder

L18 Galvanometers- oscillographs

L19 Cathode ray oscilloscopes and magnetic tape recorder

L20 Revision of 2nd

unit

L21 Electronic instruments: wave analyzer

L22 Distortion meter: Q-meter and Measurements of op-amp parameter

L23 Digital instruments: Digital indicating instruments

L24 Comparison with analog type instruments and digital display method

L25 Digital method of time and frequency measurements

L26 Digital voltmeter

L27 Revision of 3rd

unit

L28 Transducers: classification of transducers

L29 Strain guage

L30 Introduction: Displacements transducers

L31 Capacitive transducers

L32 LVDT

L33 Piezo-electric Transducers

L34 Temperature Transducer- resistance thermometer

L35 Thermocouple and Thermistors

L36 Liquid level measurements and low pressure measurements

L37 Data acquisition system: A to D and D to A convertor

L38 Analog and digital data Acquisition systems

L39 Multiplexing, spatial encoders and telemetry

L40 Revision of 4th

unit

Tutorial sheet 4

1. Write short note on data acquisition system.

2. Explain analog to digital converters.

3. Write short note on resolution.

4. Explain the term Quantization error.

5. A 100 ohm basic movement is to be used as ohmmeter requiring a full scale deflection of 1mA and

internal battery voltage of 3V. A half scale deflection marking of 2k is desired. Calculate the value of

(a) R1 and R2 (b) the maximum value of R2 to compensate for a 5% drop in battery voltage.

Tutorial sheet 5

1. Explain analog and digital data acquisition systems.

2. Write short note on multiplexing.

3. Give the detail of spatial encoder.

4. Explain the operation of basic d.c. voltmeter.

5. An ammeter reads 8.3A and true value of the current is 8.5 A. Determine the absolute error and relative

percentage error.

Tutorial sheet 6

1. Discuss working of wheat stone bridge with neat diagram.

2. Discuss Maxwell inductance Capacitance Bridge.

3. Write a short note on Wein’s bridge with circuit diagram.

4. What are temperature transducers?

5. Calculate the value of multiplier resistor for a 10 V rms ac range on the voltmeter in below figure .

Tutorial sheet 7

1. Discuss low pressure (vacumm) measurements.

2. Explain digital to analog converters.

3. Discuss working principle and operation of wave analyzer.

4. An 8 bit D/A converter has Vr = 5 V. what is output voltage when Bin = 10110100 ? Find also VLSB.

5. Write short note on thermocouple.

Tutorial sheet 8

1. Explain the working principle of oscilloscope.

2. Explain the function of trigger circuit in the oscilloscope.

3. A 0-10 A ammeter has an accuracy of 1.5 % of full scale reading. The current indicated by the ammeter

is 2.5 A. Calculate the limiting value of current and the percentage limiting error.

4. Write a short note on Carey- Foster bridge.

5. What are electronic instruments and its types.



Subject : Digital Electronics Semester : 4th

Subject Code : ECE-204E Lectures per Week : 3



SYLLABUS

UNIT 1: FUNDAMENTALS OF DIGITAL TECHNIQUES:

Digital signal, logic gates: AND. OR, NOT. NAND. NOR- EX-OR, EX-NOR, Boolean algebra.

Review of Number systems. Binary codes: BCD, Excess-3. Gray codes.

COMBINATIONAL DESIGN USING GATES:

Design using gates. Karnaugh map and Quine Mcluskey methods of simplification.

UNIT 2: COMBINATIONAL DESIGN USING MST DEVICES

Multiplexers and Demultiplexers and their use as logic elements. Decoders. Adders / Subtracters. BCD

arithmetic Circuits. Encoders. Decoders / Drivers for display devices.

SEQUENTIAL CIRCUITS:

Flip Flops: S-R- J-K. T. D, master-slave, edge triggered- shift registers, sequence generators. Counters.

Asynchronous and Synchronous Ring counters and Johnson Counter, Design of Synchronous and Asynchronous

sequential circuits.

UNIT:3 DIGITAL LOGIC FAMILIES

Switching mode operation of p-n junction, bipolar and MOS-devices. Bipolar logic families: RTL, DTL, DCTL.

HTL, TTL, ECL, MOS, and CMOS logic families. Tristate logic. Interfacing of CMOS and TTL families.

UNIT 4: A/D AND D/A CONVERTER

Sample and hold circuit, weighted resistor and R -2 R ladder D/A Converters, specifications for D/A converters.

A/D converters: Quantization, parallel -comparator, successive approximation,

counting type. Dual-slope ADC, specifications of ADCs.

PROGRAMMABLE LOGIC DEVICES: ROM, PLA. PAL, Introduction to FPGA and CPLDs.

TEXT BOOK:

1. Modem Digital Electronics (Edition III): R. P. Jain; TMH

REFERENCE BOOKS:

1. Digital Integrated Electronics: Taub & Schilling: MGH

2. Digital Principles and Applications: Malvino & Leach: McGraw Hill.

3. Digital Design: Morris Mano: PHI,

NOTE: Eight questions are to be set in all by examiner taking at least one question from each unit. Students will

be required to attempt five questions in all.

LECTURE PLAN

LECTURE No LECTURE TOPIC

L1 Introduction of Digital Electronics

L2 Digital signal, logic gates: AND. OR, NOT. NAND. NOR- EX-OR, EX-NOR

L3 Boolean algebra.

L4 Review of Number systems. Binary codes: BCD, Excess-3. Gray codes.

L5 Problems

L6 Problems

L7 Revision of 1st UNIT

L8 INTRODUCTION about COMBINATIONAL circuits

L9 Multiplexers and De-multiplexers and their use as logic elements

L10 Continuation

L11 Decoders

L12 Adders / Subtracters.

L13 BCD arithmetic Circuits.

Tutorial sheet 1

1. What is the binary equivalent of the decimal number 368?

2. What is the Decimal equivalent of hex number 1A53?

3. What is the Gray code for decimal number 6.

4. The output of a logic gate is 1 when all its inputs are at logic 0.

5. Simplify (x + y)(x + z).

Tutorial sheet 2 1. The logic circuit shown in the given figure 2 can be minimized to

2. The excess 3 code of decimal number 26 is

3. Simplify the Boolean expression F = C(B + C)(A + B + C).

4. Simplify the following expression in to sum of product using Karnaugh Map

5. F (A, B, C, D) = ∑ (1,3,4,5,6,7,9,12,13) 6. A staircase light is controlled by two switches one at the top of the stairs and another at the bottom of stairs

(i) Make a truth table for this system. (ii) Write the logic equation is SOP form.

L14 Encoders. Decoders

L15 Drivers for display devices

L16 Problems

L17 Revision of 2nd

UNIT

L18 Flip Flops: S-R- J-K. T. D,

L19 master-slave flip flop

L20 edge triggered- shift registers,

L21 Sequence generators.

L22 Counters

L23 Asynchronous and Synchronous Ring counters

L24 Johnson Counter,

L25 Design of Synchronous and Asynchronous sequential circuits

L26 Problems

L27 Revision of 3rd

UNIT

L28 Switching mode operation of p-n junction

L29 Bipolar and MOS-devices

L30 Bipolar logic families: RTL, DTL

L31 DCTL. HTL, TTL

L32 ECL, MOS

L33 CMOS logic families

L34 Tristate logic, Interfacing of CMOS and TTL families

L35 Sample and hold circuit

L36 weighted resistor and R -2 R ladder D/A Converters

L37 specifications for D/A converters

L38 A/D converters: Quantization, parallel –comparator, successive approximation

L39 Counting type, Dual-slope ADC, specifications of ADCs.

L40 ROM, PLA

L41 FPGA, CPLD

L42 REVISION 4th

UNIT

Tutorial sheet 3

1. If the input to T-flip flop is 100 Hz signal, what will be the final output of the three T-flip flops in cascade?

2. How many flip-flops are required to construct mod 30 counter

3. An eight stage ripple counter uses a flip-flop with propagation delay of 75 nanoseconds. The pulse

width of the strobe is 50ns. The frequency of the input signal which can be used for proper operation

of the counter is approximately

4. Design a 8:1 Multiplexer by using Four variable function given by

5. F(A, B, C, D) = ∑ m(0,1,3,4,8,9,15).

6. The number of control lines for a 8 – to – 1 multiplexer is

Tutorial sheet 4

1. Implement the following function using a 3 line to 8 line decoder.

i. S (A,B,C) = ∑ m(1,2,4,7)

ii. C (A,B,C) = ∑ m ( 3,5,6,7)

2. Implement the following function using 4-to-1 multiplexer.

i. Y(A,B,C) = ∑(2,3,5,6)

3. With the help of a suitable diagram, explain how do you convert a JK flip flop to T type

4. Flip flop.

5. Implement the following function using 8 to 1 multiplexer

i. Y(A,B,C,D) =∑(0,1,2,5,9,11,13,15)

6. How many Flip-Flops are required for mod–16 counter?

Tutorial sheet 5

1. What are the advantages of CMOS logic and explain CMOS Inverter with the help of a neat circuit

diagram.

2. What is Tri-state logic and explain Tri-state logic inverter with the help of a circuit diagram. Give its Truth

Table.

3. Explain the following characteristics for digital IC’s.

(i) Propagation delay

(ii) Power dissipation

4. What are the characteristics of digital ICs used to compute their performance?

5. Which of the memory is volatile memory?

Tutorial sheet 6

1. Describe CMOS inverter and state advantages of CMOS.

2. Which digital logic family has minimum power dissipation and why?

3. Which logic family has fastest logic family?

4. Which digital logic family has the lowest propagation delay time?

5. Explain the classification of Digital IC logic families.

Tutorial sheet 7

1. Find the conversion time of a Successive Approximation A/D converter which uses a 2 MHz clock and a

5-bit binary ladder containing 8V reference. What is the Conversion Rate?

2. A 6-bit R-2R ladder D/A converter has a reference voltage of 6.5V. It meets standard linearity. Find

(i) The Resolution in Percent.

(ii) The output voltage for the word 011100.

3. A 5-bit DAC produces an output voltage of 0.2V for a digital input of 00001. Find the value of the

4. output voltage for an input of 11111. What is the resolution of this DAC?

5. An 8-bit successive approximation ADC has a resolution of 20mV. What will be its digital

6. output for an analog input of 2.17V?

7. A 2-digit BCD D/A converter is a weighted resistor type with ER = 1 Volt, with R = 1MΩ, Rf = 10KΩ.

Find resolution in Percent and Volts.

Tutorial sheet 8

1. Find how many bits of ADC are required to get a resolution of 0.5 mV if the maximum full scale voltage is

10 V.

2. Compare the memory devices RAM and ROM.

3. Distinguish between ROM, PROM, EPROM, EEPROM

4. What is ROM? Is the ROM a volatile memory? Explain.

5. Find the output voltage of 4 bit ladder, having the following digital inputs 0101.



Subject : SIGNAL AND SYSTEMS Semester : 4th

Subject Code : EE-208E Lectures per Week : 3



SYLLABUS

. UNIT-I

SIGNAL

Types of signals:- Deterministic and Stochastic, periodic and a periodic, impulse functional sequences, analog

and discrete, singular functions. Signal representation in terms of singular functions, orthogonal functions and

their use in signal representation. Fourier series, Fourier and La-place transforms. Convolution theorem,

geometrical interpretation and application.

UNIT-II

Probability concepts, random variable, pdf, cdf, moments, distributions, correlation functions. Characterization

of stochastic signals.

Discretisation of analog signals – sampling, sampling theorem and its proof. Effect of under sampling,

recovery of analog signals from sampled signal. Characterization of Discrete signals in terms of impulse

sequences, Z-transforms. Properties, inversion and applications of La-place, Fourier and Z-transforms.

UNIT-III

SYSTEM

Classification linear and non-linear, time invariant and time varying, lumped and distributed. Deterministic and

Stochastic. Casual and non causal, Analog and Discrete/Digital memory and

Memory less, 1 port and N – port, SISO, SIMO, MISO, MIMO.

UNIT-IV

System modeling in terms of differential, equations, state variables, difference equations and transfer functions.

Linear time invariant system properties, elementary idea of response determination to deterministic and

stochastic signals. Concept of impulse response.

REFERENCE BOOKS:

Fred J Taylor –“Principles of Signals and System”, MGH.

Simon Haykins – “Signal & Systems”, Wiley Easter

A Papoulis – “Circuit and System” Modern Approach HRW

NOTE: Eight questions are to be set in total covering entire course selecting two questions from each unit. Each

question will be of equal marks. Students will be required to attempt five questions in all, selecting at least one

question from each unit.

LECTURE PLAN

Tutorial sheet 1

1. Given a system, which calculates the moving, average over three samples?

a) What is the impulse response?

b) What is the output y[n] of the system when the input is a unit step function?

y[n] = (x[n] + x[n-1] + x[n-2]) /3.

n ->0 1 2

13

2. Given a system described by the following recursive relation, what is its impulse response? y[n] = -0.9 y[n-

1] + x[n].

3. Given the impulse response of a causal LTI system by h[n] = αn

u[n] with |α| < 1(IIR system). What is the

output signal when the input is a unit step function?

LECTURE No. LECTURE TOPIC

L1 Introduction, Types of signals:- Deterministic and Stochastic

L2 Periodic and aperiodic, impulse functional sequences

L3 Analog and discrete, singular functions

L4 Signal representation in terms of singular functions

L5 Orthogonal functions and their use in signal representation

L6 Fourier series, Fourier and Laplace transforms

L7 Convolution theorem, geometrical interpretation and application

L8 REVISION OF 1st UNIT, Class Test

L9 Probability concepts, random variable,

L10 pdf, cdf, moments distributions,

L11 Correlation functions.

L12 Characterization of stochastic signals.

L13 Discretisation of analog signals – sampling, sampling theorem and its proof. Effect of under

sampling,

L14 Recovery of analog signals from sampled signal

L15 Characterization of Discrete signals – in terms of impulse sequences

L16 Z-transforms. Properties

L17 Inversion and applications of La-place Fourier and Z-transforms

L18 REVISION OF 2nd

UNIT

L19 Classification of systems: linear and non-linear,

L20 Time invariant and time varying

L21 Lumped and distributed

L24 Analog and Discrete/Digital memory and memory less,

L25 1 port and N – port, SISO

L26 SIMO, MISO, MIMO

L27 REVISION Of 3rd

UNIT

L28 System modeling: in terms of differential equations,

L29 State variables

L30 Difference equations

L31 Transfer functions

L32 Linear time invariant system properties

L33 Elementary idea of response

L34 Determination to deterministic and stochastic signals

L35 Concept of impulse response

L36 REVISION OF 4TH UNIT

4. What is the DFT of cos(5Ω0) with Ω0 = 2p

N ?

5. What is the DFT of a shifted signal x[n-n0]?

Denote the DFT of the shifted signal by X'[k] and of the original signal by X[k].

Tutorial sheet 2

1. Find the transfer function of the following recursive system:

y[n] = 0.9 y[n-1] + x[n].

2. Evaluating Laplace Transforms using the definition

x(t)=1 and step function x(t)=u(t)

3. Evaluate the Laplace transform of

0

)(

0

)]([ dtedteetueL tssttt

4. Find )(cos 0tL

5. Find i(t) using Laplace transform method for t>0

6. Find i(t) using Laplace transform method for t>0

Tutorial sheet 3

1. Express the signals shown in Fig. 1 in terms of unit step functions

2. The impulse response h[n] of a discrete-time LTI system. (a). Determine and sketch the output y[n]

of this system to the input x[n]. (b) Without using the convolution technique.

3. Consider the discrete-time system. Write a difference equation that relates the output y[n] and the input

x[n].

4. Distinguish between Continuous time and discrete time signals

5. Distinguish between Periodic and Non periodic Signals

Tutorial sheet 4

1. Find the even and odd components of x (t) = ejt.

2. Show that the product of two even signals or of two odd signals is an even signal and that the product of an

even and an odd signal is an odd signal.

3. Given the signal x(t) as shown in fig 1.b, sketch the following:

i) X(-2t+3)

ii) X(t/2 -2)

4. A continuous-time signal x ( t ) is shown in Fig. 1-17. Sketch and label each of the following signals. ( i )

x(t - 2); ( ii) x(2t); ( iii ) x ( t / 2 ) ; (iv)l x ( - t )

5. Determine the discrete-time convolution sum of the given sequences’(n) =1, 2, 3, 4 and h(n)= 1, 5, 1

Tutorial sheet 5

1. Find the Fourier transform of x [ n ] = - an u[-n-1]

2. Show that the real and odd continuous time non periodic signal has purely imaginary

Fourier transforms.

3. For the following signals, (i) determine analytically which are periodic (if periodic, give the period) and (ii)

sketch the signals. (Scale your time axis so that a sufficient amount of the signal is being plotted.).

a) x(t) = 4 cos(5t)

b) x(t) = 4 cos(5t-/4)

4. Give an expression for the signal

5. Write an expression for the waveform f(t) shown in Fig. using only unit step function and powers of t.

Tutorial sheet 6

1. Define a unit impulse function δ(t).

2. Find the Laplace transform of t sinw0t u(t )

3. Find the inverse Laplace transform of3

2

( 1)

s

s s

4. Find the impuse response of a system characterized by the differential equation ( ) ( ) ( )y t ay t x t

5. Sketch the function ( ) (sin ) ( sin )t t

f t u uT T

Tutorial sheet 7

1. A linear system H has an input-output pair as shown in Fig. Determine whether the System is causal and

time-invariant.

2. Find the difference equation describing the system represented by the block-diagram Shown in Fig.3, where

D stands for unit delay

3. Is it possible for a non causal system to possess memory? justify your answer

4. Determine the Z-Transform of

1

2

( ) ( )

( ) ( 1)

n

n

x n u n

x n u n

and include its region of convergence

5. Let the Z-transform of x(n) be X(Z).Show that the z-transform of x(-n) is X(1/Z)

Tutorial sheet 8

1. A linear time invariant system may be causal or non causal. Give an example of each of these possibilities

2. For the simple continuous time RC frequently selective filter shown in fig 4.obtain the frequency response

H(w).Sketch the magnitude and phase for -∞<w<∞

3. An LTI system is characterized by the difference equation: x(n – 2) – 9x(n – 1) + 18x(n)= 0 with initial

conditions x(-1) = 1 and x(-2) = 9. Find x(n) by using z-transform and state the properties of z-transform

used in your calculation.

4. Given that y(t ) = x(t )* h(t ), determine x(at )* h(at ) in terms of y(t ). If a is real, for what values of a the

system will be (i) causal, (ii) stable?

5. Find the even and odd parts of the following functions

a. ( ) sinf t t t

b. 2

0 1 2( )f t a a t a t



Subject : FIELD AND WAVES Semester : 4th

Subject Code : EE-206E Lectures per Week : 3



SYLLABUS

UNIT-1

ELECTRIC FIELD AND CURRENT

Coulomb's law. Electric field intensity, field due to a continuous volume charge distribution, field of a line

charge, field of a sheet of charge, electric flux density, Gauss's law and applications, electric potential, the

dipole, current density, continuity of current, metallic conductors, conductor properties and boundary

conditions, the method of images, the nature of dielectric materials, boundary conditions for perfect dielectric

materials, capacitance of two wire line, Poisson's and Laplace’s equations, uniqueness theorem.

UNIT-II

MAGNETIC FIELD AND MAXWELL EQUATION

Biot - Savart law. Ampere's law, magnetic vector potentials, force on a moving charge, differential current

element, force and torque on a closed circuit, the boundary conditions, the magnetic circuit, potential energy and

forces on magnetic materials. Faraday's law, Maxwell's equations in point form and integral form Maxwell's

equations for sinusoidal variations, retarded potentials.

UNIT-III

THE UNIFORM PLANE WAVE

Wave motion in free space and perfect dielectrics, plane waves in lossy dielectrics. The Poynting vector and

power considerations, propagation in good conductors, skin effect, reflection of uniform plane waves, SWR.

UNIT-IV

TRANSMISSION LINES AND WAVEGUIDES

The Transmission line equations, graphical methods, Smith chart, time-domain and frequency domain analysis.

TE, TM, TEM waves, TE and TM modes in rectangular and circular waveguides, cut-off and guide wavelength,

wave impedance and characteristic impedance, dominant modes, power flow in waveguides, excitation of

waveguides, dielectric waveguides.

REFERENCES:

1. Jordan E C & Balmain K G, Electromagnetic Waves and Radiating Systems, PHI.

2. David K. Chang, Field and Waves Electromagnetics, Addison Wesley.

3. Hayt W H JR., Engineering Electromagnetics, Tata McGraw Hill, Fifth edition.

NOTE:

Eight questions are to be set in all by the examiner taking two questions from each unit. Students will be

required to attempt five questions in all selecting at least one question from each unit. Each question will be of

equal marks.

LECTURE PLAN

LECTURE No. LECTURE TOPIC

L1 Coulomb's law, Electric field intensity

L2 field due to a continuous volume charge distribution

L3 Field of a line charge, field of a sheet of charge L4 electric flux density, Gauss's law and applications, electric potential L5 The dipole, current density L6 continuity of current, L7 metallic conductors L8 conductor properties and boundary conditions

Tutorial sheet 1

1. The value of E at 0( 2, 40 , 3)P z is given as 100 200 300 /zE a a a V m .

Determine the incremental work required to move a 20 C charge a distance of 6 m in the direction

of : (a) a ; (b) a ; (c) za ; (d) E; (e) 2 3 4x y zG a a a

2. Find the amount of energy required to move a 6-C charge from the origin to P(3,1,-1) in the field

E=2xax-3y2ay+4az V/m along the straight line path x= -3z, y=x+2z.

3. A uniform surface charge density of 20nC/m2 is present on the spherical surface r= 0.6cm in free space.

(a) Find the absolute potential at0 0( 1 , 25 , 50 )P cm . (b) Find VAB, given points

0 0(2 , 30 , 60 )A cm and 0 0(3 , 45 , 90 )B cm

4. Two uniform line charges, 8nC/m each, are located at x=1, z=2, and at x=-1, y=2, in free space. If the

potential at the origin is 100V, find V at P(4,1,3)

5. The non uniform linear charge density,28/( 1) /L z nC m , lies along the z-axis. Find the

potential at ( 1,0,0)P in free space if V=0 at .

6. Let V=2xy2z

3 and 0 . Given point P(1,2,-1), find: (a) V at P; (b) E at P; (c) v at P; (d) the

equation of the streamline passing through P; (f) Does V satisfy Lap

L9 The method of images

L10 The nature of dielectric materials, boundary conditions for perfect dielectric materials L11 Capacitance of two wire line, Poisson's and Lap lace’s equations L12 Uniqueness theorem

L13 Revision of Unit I

L14 Biot - Savart law. Ampere's law

L15 magnetic vector potentials

L16 force on a moving charge, differential current element L17 force and torque on a closed circuit L18 the boundary conditions, the magnetic circuit L19 potential energy and forces on magnetic materials

L20 Faraday's law, Maxwell's equations in point form

L21 integral form Maxwell's equations for sinusoidal variations L22 skin effect, reflection of uniform plane waves L23 SWR

L24 retarded potentials

L25 Revision of Unit II

L26 Wave motion in free space L27 Wave motion in perfect dielectrics

L28 plane waves in lossy dielectrics

L29 The Poynting vector and power considerations L30 Propagation in good conductors

L31 Revision of Unit III

L32 The Transmission line equations

L33 Time domain and frequency domain analysis. TE, TM, TEM waves L34 TE and TM modes in rectangular and circular wave guides, cut-off and guide wavelength L35 wave impedance and characteristic impedance

L36 dominant modes, power flow in waveguides

L37 Excitation of waveguides

L38 Dielectric waveguides. L39 graphical methods, Smith chart L40 Revision of Unit IV

Tutorial sheet 2

1. (a) Find H in Cartesian components at P (2, 3, 4) if there is a current filament on the z-axis carrying

8mA in the az direction. (b) Repeat if filament is located at x=-1, y=2. (c) Find H if both filaments are

present.

2. A current sheet K=8ax A/m flows in the region -2 < y < 2m in the plane z=0. Calculate H at P (0, 0, 3).

3. Assume that there is a region with cylindrical symmetry in which the conductivity is given

by1501.5 /e kS m . An electric field of 30az V/m is present. (a) Find J. (b) Find the total current

crossing the surface 0 , z=0, all . (c) Make use of Ampere’s circuital law to find H.

4. A point charge, Q=-0.3 C and m=3X10-16

kg, is moving through the field E=30az V/m. Develop the

appropriate differential equations and solve them, subject to the initial conditions at t=0; v=3X105axm/s

at the origin. At t=3 s , find : (a) the position P(x, y, z) of the charge; (b) the velocity v; (c) the

kinetic energy of the charge.

5. Uniform current sheets are located in free space as follows: 8az A/m at y=0, -4az A/m at y=1, and -4az

A/m at y=-1. Find the vector force per meter length exerted on a current filament carrying 7mA in the

aL direction if the filament is located at: (a) x=0, y=0.5, and aL=az; (b) y=0.5, z=0, and aL=ax; (c) x=0,

y=1.5, and aL=az

Tutorial sheet 3

1. A uniform plane wave in air, 10

1 10 cos(10 ) / ,x xE E t z V m is normally incident on a copper

surface at z=0. What percentage of the incident power density is transmitted into the copper?

2. The magnetic field intensity in a region where ' ' =0 is given as H 5cos cos yH t z a A/m,

where =5Grad/s and =30rad/m. If the amplitude of the associated electric field intensity is 2kV/m,

find: (a) and ' for the medium; (b) E.

3. A wave starts at point a, propagates 100m through a lossy dielectric for which 0.5 , reflects at

normal incidence at a boundary at which 0.3 0.4j , and then returns to point a. Calculate the

ratio of the final power to the incident power after this round trip.

4. A 150 MHz uniform plane wave is normally incident from air onto a material whose intrinsic

impedance is unknown. Measurements yield a standing wave ratio 0f 3 and the appearance of an

electric field minimum at 0.3 wavelengths in front of the interface. Determine the impedance of the

unknown material.

5. A uniform plane wave in air is normally incident onto a lossless dielectric plate of thickness / 8 , and

of intrinsic impedance 260 . Determine the standing wave ratio in front of the plate. Also find

the fraction of the incident power that is transmitted to the other side of the plate.

Tutorial sheet 4

1. The parameters of a certain transmission line operating at 6X108 rad/s and L=0.4 /H m , c=pF/m,

G=80mS/m, and R=20ohm/m. (a) Find 0, , ,and Z . (b) If a voltage wave travels 20m down the

line, by what percentage is its amplitude reduced, and by how many degrees is its phase shifted?

2. The characteristic impedance of a certain lossless transmission line is 72 . If L=0.5 /H m , find:

(a) C; (b) Vp; (c) if f=80MHz (d) The line is terminated with a load of 60 . Find and s.

3. A parallel –plate waveguide is known to have cutoff wavelength for the m=1 TE and TM modes of

1c =0.4cm. The guide is operated at wavelength =1mm. How many modes propagate?

4. A parallel – plate guide is to be constructed for operation in TEM mode only over the frequency range

0 < f < 3GHz. The dielectric between plates is to be Teflon ('

R =2.1). Determine the maximum

allowable plate separation, d.

5. Two characteristics of a certain lossless transmission line are Z0=50ohm and 10 0.2j m at

f=60MHz: (a) find L and C for the line. (b) A load ZL = 60+j80 ohm is located at z=0. What is the

shortest distance from the load to a point at which Zin= Rin+j0 ?

Tutorial sheet 5

1. The annular surface, 1cm < < 3cm, z=0, carries the non uniform surface charge density s =5

nC/m2. Find V at P (0,0,2cm) if V = 0 at infinity.

2. Let V= 2xy2z

3+3ln(x

2+2y

2+3z

2)V in free space. Evaluate each of the following quantities at P (3,2,-1):

(a) V; (b) V ; (c) E; (d) E ; (e) aN; (f) D

3. It is known that the potential is given as V= 80r0.6

V. Assuming free space conditions, find: (a) E; (b)

the volume charge density ar r=0.5m; (c) the total charge lying within the surface r=0.6.

4. A dipole having a moment p = 3ax-5ay+10az nC.m is located at Q(1,2,-4) in free space. Find V at

P(2,3,4).

5. Four 0.8-nC point charges are located in free space at the corners of a square 4cm on a side. (a) Find

the total potential energy stored. (b) A fifth 0.8- C charge is installed at the corner of the square.

Again find the total stored energy.

6. Given the potential field V= (A4 +B

4 )sin4 : (a) show that

2 0V ; (b) select A and B so that

V=100V and E = 500V/m at 0( 1, 22.5 , 2)P z .

Tutorial sheet 6

1. A current filament of 3ax A lies along the x axis. Find H in cartesian components at p(-1,3,2)

2. Let a filamentary current of 5mA be directed from infinity to the origin on the positive z axis and then

back out to infinity on the positive x axis. Find H at P(0,1,0).

3. A current filament on the z axis carries a current of 7mA in the az direction, and current sheets of 0.5az

A/m and -0.2az A/m are located at =1 cm and = 0.5 cm, respectively. Calculate H at =: (a)

0.5cm; (b) 1.5cm; (c) 4cm; (d) What current sheet should be located at =4cm so that H=0 for all

>4cm?

4. A rectangular loop of wire in free space joins points A(1,0,1) to B(3,0,1) to C(3,0,4) to D(1,0,4) to A.

The wire carries a current of 6mA, flowing in the az direction from B to C. A filamentary current of 15

A flows along the entire z axis in the az direction. (a) Find F on the side BC. (b) Find F on the side AB.

(c) Find FTotal on the loop.

5. A current of 6 A flows from M(2,0,5) to N(5,0,5) in a straight solid conductor in free space. An infinite

current filament lies along the z axis and carries 50 A in the az direction. Compute the vector torque on

the wire segment using an origin at: (a) (0,0,5); (b) (0,0,0); (c) 3,0,0.

Tutorial sheet 7

1. The plane y=0 defines the boundary between two different dielectrics. For y < 0, '

1R =1, 1 0 , and

' '

1R =0; and for y > 0, '

2R =5, 2 0 , and ' '

2R =0. Let 1 150cos( 8 ) /zE t y V m , and find:

(a) ; (b) 1H ; (c) 1H

2. A 50 MHz uniform plane wave is normally incident from air onto the surface of a calm ocean. For

seawater, =4 S/m, and '

R =78. (a) Determine the fractions of the incident power that are reflected

and transmitted. (b) Qualitatively, how many will these answers change (if at all) as the frequency is

increased?

3. A right- circularly polarized plane wave is normally incident from air onto a semi-infinite slab of

plexigals (' 3.45R ,

' ' 0R ). Calculate the fractions of the incident power that are reflected and

transmitted. Also, describe the polarizations of the reflected and transmitted waves.

4. Region 1, Z< 0, and region 2, z > 0, are both perfect dielectrics ( 0 ,' ' 0 ). A uniform plane

wave travelling in the az direction has a radian frequency of 3X 1010

rad/s. Its wavelengths in the two

regions are 1 5cm and 2 3cm . What percentage of the energy incident on the boundary is : (a)

reflected; (b) transmitted; (c) What is the standing wave ratio in region 1?

5. In figure 12.1, let region 2 be free space, while 1 1R , ' '

1 0R , and '

1R is unknown. Find '

1R if:

(a) the amplitude of 1E

is one- half that of 1E

; (b) 1,av is one-half of 1,av

; (c) 1 minE is one-half

of 1 maxE

Tutorial sheet 8

1. A lossless transmission line with Z0 = 60ohm is being operated at 60MHz. The velocity on the line is

3X108 m/s. If the line is short circuited at z=0, find Zin at z=: (a) -1m; (b) -2m; (c) -2.5m; (d) -1.25m.

2. A lossless transmission line having Z0=120ohm is operating at w=5X108 rad/s. If the velocity on the

line is 2.4X108 m/s, find; (a) L; (b) C; (c) Let ZL be represented by an inductance of 0.6 H in series

with a 100-ohm resistance. Find and s.

3. The propagation constant of a lossy transmission line is 1+j2 m-1

, and its characteristic impedance is

20+j0 ohm at w=1 Mrad/s. Find L, C, R, and G for the line.

4. A lossless parallel-plate waveguide is known to propagate the m=2TE and TM modes at frequencies as

low as 10GHz. If the plate separation is 1 cm, determine the dielectric constant of the medium between

plates.

5. The cutoff frequency of the m= 1TE and TM modes in a parallel- plate guide is known to be

fc1=7.5GHz. The guide is used at wavelength =1.5cm. Find the group velocity of the m=2 TE and

TM modes.



Subject : ELECTRONICS MEASUREMENTS LAB Semester : 4th

Subject Code : EE-208E Lectures per Week : -

Viva Marks : 50 Tutorials per Week : -

Sessional Marks : 50 Practical : 3

LIST OF EXPERIMENTS

1. To measure the unknown Inductance in terms of capacitance and resistance by using Maxwell’s

Inductance bridge.

2. To measure unknown Inductance using Hay’s bridge.

3. To measure unknown capacitance of small capacitors by using Schering’s bridge.

4. To measure 3-phase power with 2-Wattmeter method for balanced and unbalanced bridge.

5. To measure unknown capacitance using De-Sauty’s bridge.

6. To measure unknown frequency using Wein’s frequency bridge.

7. To measure unknown low resistance by Kelvin’s Double bridge.

8. To test the soil resistance using Meggar (Ohm meter).

9. To calibrate Energy meter using standard Energy meter.

10. To plot the B-H curve of different magnetic materials.

11. To calibrate the Voltmeter using Crompton Potentiometer.

12. To convert the Voltmeter into Ammeter using Potentiometer.

13. Insulation testing of cables using Digital Insulation Tester.

NOTE:

At least eight experiments are to be performed from above list and the concerned institution as per the scope of

the syllabus can set remaining two



Subject : DIGITAL ELECTRONICS LAB Semester : 4th

Subject Code : EE-210E Lectures per Week : -



LIST OF EXPERIMENTS

1. Familiarization with Digital Trainer Kit and associated equipment.

2. Study of TTL gates AND, OR, NOT, NAND, NOR, EX-OR, EX-NOR.

3. Design and realize a given function using K-Maps and verify its performance.

4. To verify the operation of Multiplexer and Demultiplexer.

5. To verify the operation of Comparator.

6. To verify the truth table of S-R, J-K, T, D Flip-flops.

7. To verify the operation of Bi-directional shift register.

8. To design and verify the operation of 3-bit asynchronous counter.

9. To design and verify the operation of asynchronous Up/down counter using J-K FFs.

10. To design and verify the operation of asynchronous Decade counter.

11. Study of TTL logic family characteristics.

12. Study of Encoder and Decoder.

13. Study of BCD to 7 segment Decoder.

NOTE:


the syllabus can set remaining two.

\



Subject : COMPUTATIONAL TECHNIQUES LAB Semester : 4th

Subject Code : MAT-206E Lectures per Week : -



LIST OF EXPERIMENTS 1. Solution of Non-Linear Equation in single variable using the method of successive Bisection.

2. Solution to non-linear equation in single variable using the Newton-Raphons method.

3. Solution to non linear equation in single variable using the Secant method.

4. Solution to a system of simultaneous algebraic equations using the Gaussian elimination procedure.

5. Solution to a system of simultaneous algebraic equations using the Gauss-Seidel iterative method.

6. Numerical solution to an ordinary differential equation using the Eulers method.

7. Numerical solution to an ordinary differential equation using the Runge-Kutta Method.

8. Numerical solution to an ordinary differential equation using the Predictor Corrector Method.

9. Numerical Solution to the Laplace equation using the method of finite differences.

10. Solution to system of simultaneous equations using Gauss-Seidal iterative method employing the

technique of successive relaxation.

NOTE:


the syllabus can set remaining two.

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