# Syllabus of Second year Electronics Engineering - Mumbai University

The Syllabus of Second year Electronics Engineering is given in detail the marks distribution along with the books recommended by Mumbai university.

### Mumbai University Electronic Engineering syllabus

**S.E. (ELECTRONICS) MUMBAI UNIVERSITY**

SEMESTER III

[1] Electronic Circuit Analysis & Design I

SEMESTER III

[1] Electronic Circuit Analysis & Design I

Lectures: 4 hours / week

Theory Paper: 3 hours and 100 marks

Practicals: 3 hours / week

Termwork: 25marks

Electronic Circuit Analysis & Design I

Lectures: 4 hours / week

Theory Paper: 3 hours and 100 marks

Practicals: 3 hours / week

Termwork: 25marks

Rationale:

The subject of Electronic circuit design I shall lay a strong fundamental base in discrete electronics. The emphasis shall be on design of basic electronic circuits. The scope of the subject is completely covered by the textbooks mentioned.

Semiconductor Materials and Diodes

Review of Semiconductor Materials and Properties, The PN Junction, Introduction to Semiconductor Diode Theory. Diode Circuits: DC Analysis and Models, AC Equivalent Circuits, Other Diode Types – Solar Cell, Photodiode, Light–Emitting Diode, Schottky Barrier Diode, Zener Diode, Temperature Effects, Understanding Manufacturer's Specifications.

Diode Circuits

Design of Rectifier Circuits, Half Wave Rectification, Full Wave Rectification, Filter, Ripple Voltage and Diode Current, Voltage Doubler Circuit, Zener Diode Circuits, Clipper and Clamper Circuits, Multiple–Diode Circuits, Photodiode and LED Circuits.

The Bipolar Junction Transistor

Basic Bipolar Junction Transistor, Transistor Structures, NPN Transistor : Forward–active Mode Operation, PNP Transistor : Forward–active Mode Operation, Circuit Symbols and Conventions, Current–Voltage Characteristics, Non ideal Transistor Leakage Currents and Breakdown, DC Analysis of Transistor Circuits, Common–Emitter Circuits, Load Line and Modes Of Operation, Common Bipolar Circuits: DC Analysis, Basic Transistor Applications – Switch, Amplifier, Bipolar Transistor Biasing – Single Base Resistor Biasing, Voltage Divider Biasing and Bias Stability, Integrated Circuit Biasing, Multistage Circuits.

Basic BJT Amplifiers

Analog Signals and Linear Amplifiers, The Bipolar Linear Amplifier, Graphical Analysis and AC Equivalent Circuit, Small Signal Hybrid – π Equivalent Circuit of the Bipolar Transistor, Hybrid – π Equivalent Circuit Including the Early Effect, Expanded Hybrid – π Equivalent Circuit, Other Small – Signal Parameters And Equivalent Circuits, Basic Transistor Amplifier Configurations, Common Emitter Amplifiers, AC Load Line Analysis, Common Collector Emitter Follower Amplifier, Common Base Amplifier, The Three Basic Amplifier configurations: Summary and Comparison, Multistage Amplifiers, Power Considerations, Environmental Thermal Considerations in Transistor Amplifiers, Manufacturers' Specifications.

The Field Effect Transistor

Junction Field–Effect Transistor, MOS Field–Effect Transistor, MOSFET DC Circuit Analysis, Basic MOSFET Applications: Switch, Digital Logic Gate and Amplifier. Temperature effects in MOSFETs, Input Protection in MOSFET. The Power FET (VMOS).

Basic FET Amplifiers

The MOSFET Amplifier, Basic Transistor Amplifier Configurations, the Common Source Amplifier, The Source Follower Amplifier, The Common Gate Configuration, The Three Basic Amplifier Configuration: Summary and Configuration, Single – Stage Integrated Circuit MOSFET Amplifiers, Multistage Amplifiers, Basic JFET Amplifiers

**Text Books:**

1. Donald A. Neamen, Electronic Circuit Analysis and Design, Second edition, McGraw Hill International edition 2001

2. Martin Roden , Gordon Carpenter, William Wieserman, Electronic Design, Fourth edition, Shroff Publishers, 2002

Additional Reading:

1. Donald Schilling & Charles Belove, Electronic Circuits Discrete and Integrated, Third edition, McGraw Hill International edition, 1989

Termwork:

The termwork shall consist of atleast six laboratory experiments covering the whole of syllabus, duly recorded and graded as well as atleast four computer simulations using EDA tools like PSPICE duly recorded and graded. This will carry a weightage of fifteen marks. A test shall be conducted and will carry a weightage of ten marks.

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[2]Electronic Circuit Analysis & Design II

[2]Electronic Circuit Analysis & Design II

Lectures: 4 periods /week

Theory Paper: 3 hours and 100 marks

Practicals: 3 periods /week

Termwork: 25marks;

Oral*: 25 marks;

Practical*: 25 marks

Rationale:

The subject of Electronic circuit design II shall lay a strong fundamental base in discrete electronics which will help the student to grasp concepts of integrated circuits easily. The emphasis shall be on design of basic electronic circuits. The scope of the subject is completely covered by the textbooks mentioned.

Frequency Response of Amplifiers

Amplifier Frequency Response, System Transfer Functions, S – Domain Analysis, First – Order Functions, Bode Plots, Short–Circuit and Open–Circuit Time Constants, Frequency Response: Transistor Amplifiers with Circuit Capacitors, Frequency Response: Bipolar Transistor, Frequency Response: The FET, High Frequency Response of Transistor Circuits. Sinusoidal Oscillators: The phase shift Oscillator, The Wien Bridge Oscillator, The Tuned Circuit Oscillator, The Colpitts Oscillator and Hartley Oscillator.

Output Stage and Power Amplifiers

Power Amplifiers, Power Transistors – Power BJTs, Power MOSFETs, Heat Sinks, design of heat sinks, Classes Of Amplifiers – Class–A Operation, Class–B Operation, Class–AB Operation, Class–C Operation, Class–A Power Amplifiers, Class–AB Push Pull Complementary Output Stages.

Differential and Multistage Amplifiers

The Differential Amplifier, Basic BJT Differential Pair, Basic FET Differential Pair, Differential Amplifier with Active Load, BICMOS Circuits, Gain Stage and Simple Output Stage, Simplified BJT Operational Amplifier Circuit, Differential Amplifier Frequency Response. The Darlington Amplifier and Cascode Amplifier.

Feedback and Stability

Introduction to Feed Back, Basic Feedback Concepts, Ideal Close–Loop Gain, Gain Sensitivity Bandwidth Extension, Noise Sensitivity, Reduction of Nonlinear Distortion, Ideal Feedback Topologies, Series–Shunt, Shunt–Series, Series–Series, Shunt–Shunt Configurations, Voltage (Series – Shunt) Amplifiers, Current (Shunt – Series) Amplifiers, Trans Conductance (Series – Series) Amplifiers, Trans Resistance (Shunt – Shunt) Amplifiers, Loop Gain, Stability of The Feedback Circuit, The Stability Problem, Bode Plots: One – Pole, Two – Pole, and Three – Pole Amplifiers, Nyquist Stability Criterion, Phase and Gain Margins, Frequency Compensation Basic Theory, Closed Loop Frequency Response, Miller Compensation.

**Text Books:**

1. Donald A. Neamen, Electronic Circuit Analysis and Design, Second edition, McGraw Hill International edition 2001

2. Martin Roden , Gordon Carpenter, William Wieserman, Electronic Design, Fourth edition, Shroff Publishers, 2002

Additional Reading:

1. Donald Schilling & Charles Belove, Electronic Circuits Discrete and Integrated, Third edition, McGraw Hill International edition, 1989

2. Adel Sedra & Kenneth Smith, Microelectronic Circuits, Fourth edition, Oxford University Press, 1998

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Termwork:

The termwork shall consist of atleast six laboratory experiments covering the whole of syllabus, duly recorded and graded as well as atleast four computer simulations using EDA tools like PSPICE duly recorded and graded. This will carry a weightage of fifteen marks. A test shall be conducted and will carry a weightage of ten marks.

* Oral and Practical examination will be based on Electronic Circuit Analysis & Design I and Electronic Circuit Analysis & Design II subjects taken together.

**[3]Basics of Communication Engineering**

Lectures: 3 hours / week

Theory Paper: 3 hours and 100 marks

Practical: 3 hours / week

Term work: 25 marks

Rationale

This first subject on telecommunication shall lay a strong base on basic principles in communication systems. It introduces concepts of different communication systems and techniques which would be useful in advanced courses on communication.

Introduction:

Elements of a communication system, modulation and demodulation.

Noise in Communication systems, Signal-to-Noise ratio, Noise factor and Noise Figure, Equivalent Noise Temperature.

Amplitude Modulation:

DSB Full carrier AM – principles, modulator circuits, transmitters. Different types of AM, Suppressed – carrier AM, SSB, ISB – Principles, transmitters.

Angle Modulation:

Frequency modulation, Phase modulation, Effect of noise, FM modulators, Transmitters.

Radio receivers:

Receiver characteristics, TRF and Superheterodyne receivers, AM detectors, FM detectors, Receiver circuits.

Radio wave propagation:

Electromagnetic waves, Properties of radio waves, Propagation of waves, Propagation terms and definitions.

Analog Pulse Modulation:

Sampling Theorem for Low – pass and Band – pass signals – proof with spectrum, Aliasing. Sampling Techniques – principle, generation, demodulation, spectrum. PAM, PWM, PPM – generation and detection.

Digital Transmission:

Quantization, Quantization error, Non-uniform quantizing, Encoding. PCM, DPCM, Delta modulation, Adaptive Delta modulation – transmission system, bandwidth.

Multiplexing:

TDM, FDM – Principles, Hierarchy.

Text Books:

Text Books:

1. Wayne Tomasi, Electronic Communication Systems, Pearson Education, third edition, 2001.

2. Roy Blake, Electronic Communication Systems, Thomson Asia Pte. Ltd., Singapore, second edition, 2002.

3. Leon W Couch, Digital and Analog Communication Systems, Pearson Education, sixth edition.

4. Herbert Taub and Donald Schilling, Principles of Communication Systems, Tata McGraw-Hill, second edition.

(Text books 3 & 4 for Digital transmission and Multiplexing topics only)

Termwork:

The Termwork shall consist of at least eight experiments based on the whole syllabus, duly recorded and graded. This will carry a weightage of fifteen marks. A test shall be conducted and will carry a weightage of ten marks.

**[4]Digital Design I**

Lectures: 3 hours / week

Theory Paper: 3 hours and 100 marks

Practicals: 2 hours / week

Termwork: 25marks

Rationale

The Digital Design I subject shall lay a strong base in basic principles of digital design that do not change with technology. The subject shall also wed these basic principles with tools and practical techniques that teach how to design for today's technology. These include the VHDL design language. The emphasis will be on combinational circuits.

Introduction to digital systems

Analog VS Digital systems, digital devices, integrated circuits, programmable logic devices, digital design levels, software aspects of digital design.

Number systems and codes

Positional number systems, Binary and Hexadecimal number systems, general positional number systems conversions, arithmetic operations, representation of negative numbers, arithmetic operations on signed numbers, binary and gray codes, character codes, codes for detecting and correcting errors.

Logic circuits

Logic signals and gates, Boolean Algebra, theorems, combinational circuit analysis, combinational circuit synthesis – minimization, Karnaugh Maps, sum of products and product of sums expressions and their minimization, programmed minimization methods – Quine McCluskey minimization algorithm, timing hazards – static and dynamic hazards, introduction to VHDL hardware description language.

Combinational logic design practices

Documentation standards, Circuit timing, Combinational PLDs. Design using SSI and MSI devices Decoders, Encoders, Three state buffers, Multiplexers, Parity circuits, Comparators, Adders, Subtractors, ALUs, Combinational multipliers. Using VHDL and PLDs Combinational circuit design examples – barrel shifter, simple floating – point encoder, cascading comparator.

Logic families

CMOS logic; MOS transistors review, basic CMOS inverter circuit, CMOS NAND and NOR gates, fan – in, fan – out, Electrical behavior of CMOS circuits, propagation delay, power consumption, multi source busses, CMOS logic families, bipolar logic introduction, review of BJT, TTL NAND and NOR gates, fan – in, fan – out, Electrical behavior of TTL circuits, propagation delay, power consumption. CMOS / TTL interfacing, Introduction to Emitter – coupled logic. Interpreting Manufacturers' data sheets

Sequential logic principles

Bistable elements, Latches and flip–flops, S-R latch, D latch, Edge triggered D flip–flop, Master/slave flip–flops, T flip–flop.

**Textbooks:**

1. John F. Wakerley, Digital Design Principles and Practices, third edition updated, Pearson Education Singapore, 2002.

2. Stephen Brown & Zvonko Vranesic, Fundamentals of Digital logic with VHDL design, first edition, McGraw Hill International edition, 2000.

Additional Reading:

3. Robert K. Dueck, Digital Design with CPLD Applications and VHDL, Thomson Asia Pte. Ltd., Singapore, 2001.

4. Alan B. Marcovitz, Introduction to logic design, first edition, McGraw Hill International edition 2002.

5. James Bignell & Robert Donovan, Digital Electronics, fourth edition, Thomson Asia Pte. Ltd., Singapore, 2001.

Termwork:

The termwork shall consist of atleast six laboratory experiments covering the whole of syllabus, duly recorded and graded as well as atleast four computer simulations using VHDL, duly recorded and graded. This will carry a weightage of fifteen marks. A test shall be conducted and will carry a weightage of ten marks.

**[4]Digital Design II**

Lectures: 3 hours / week

Theory Paper: 3 hours and 100 marks

Practicals: 2 hours / week

Termwork: 25marks; Practical: 25 marks;

Oral*: 25 marks

Rationale

The subject Digital Design II subject shall lay a strong base in Sequential circuits and sequential circuit design. Modern concepts of testability and reliability are also covered.

Sequential logic design

Clocked synchronous state machine analysis, Clocked synchronous state machine design, designing state machines using state diagrams, state machine synthesis using transition lists, decomposing state machines, feedback sequential circuits, VHDL sequential circuit design features.

Sequential logic design practices

Sequential circuit documentation standards, use of latches and flip–flops in examples like switch de-bouncing, bus holder circuit, counters – ripple and synchronous, MSI counters and applications, decoding binary counter states, counters in VHDL. Shift registers, structure, MSI shift registers, serial / parallel conversion, shift register counters, ring counters, Johnson counters, linear feedback shift register counters, shift registers in VHDL. Synchronous design methodology, impediments to synchronous design, synchronizer failure and metastability. Design examples like a few simple machines, and traffic light controller, done in VHDL.

Memory, CPLDs and FPGAs

Types of memory devices, Read-Only Memory (ROM), Read / write memory, Static RAM, Dynamic RAM, Introduction to Xilinx XC9500 CPLD family and Xilinx XC 4000 FPGA family.

Additional topics

Computer Aided Design (CAD) tools, Concept of design for testability, concept of digital system reliability, introduction to transmission lines, reflections and termination.

**Textbooks:**

1. John F. Wakerley, Digital Design Principles and Practices, third edition updated, Pearson Education Singapore, 2002.

2. Stephen Brown & Zvonko Vranesic, Fundamentals of Digital Logic with VHDL Design, first edition, McGraw Hill International edition, 2000.

Additional Reading:

1. John M. Yarbrough, Digital Logic Applications and Design, first edition, Thomson Asia Pte. Ltd., Singapore, 2001

Termwork:

The termwork shall consist of atleast six laboratory experiments covering the whole of syllabus, duly recorded and graded as well as atleast four computer simulations using VHDL, duly recorded and graded. This will carry a weightage of fifteen marks. A test shall be conducted and will carry a weightage of ten marks.

* Oral examination will be based on Digital Design I and Digital Design II subjects taken together.

**[5]Electrical Network Analysis & Synthesis**

Rationale

The subject Electrical Network Analysis & Synthesis lays a base for many subjects like Electronic Circuit Design I & II, Control System Engineering, Analog Integrated Circuits & applications and Continuous Time Signals and Systems. It involves understanding basic fundamentals of network, and applying efficient tools for its analysis. The subject also involves concepts of network synthesis.

Lectures: 3 hours / week

Theory Paper: 3 hours and 100 marks

Practicals: 2 hours / week

Termwork: 25marks

Review

D.C. & A.C circuits.

Mesh & Node Analysis

Mesh & Node Analysis of circuits with independent & dependent sources.

Linearity, Superposition & Source Transformation

Linearity, Superposition, Current & Voltage Source Transformation.

Network Theorems

Thevenin's & Norton's Theorem (with independent & dependent sources), Maximum power transfer theorem.

Circuit Analysis

Introduction to Graph Theory. Tree, link currents, branch voltages, cut set & tie set.

Mesh & Node Analysis, Gauss Elimination Technique, Duality.

Time & Frequency Response of Circuits

First & second Order Differential equations, initial conditions. Evaluation & analysis of Transient and Steady state responses using Classical Technique as well as by Laplace Transform (for simple circuits only). Transfer function, Concept of poles and zeros. Frequency response of a system (concepts only).

Two - port Networks

Concept of two- port network. Driving point & Transfer Functions, Open Circuit impedance (Z) parameters, Short Circuit admittance (Y) parameters, Transmission (ABCD) parameters. Inverse Transmission (A'B'C'D') parameters. Hybrid (h) parameters. Inter Relationships of different parameters. Interconnections of two - port networks. T & Pi representation. Terminated two - port networks.

Fundamentals of Network Synthesis

Positive real functions, Driving Point functions, Brono's Positive real functions, Properties of Positive real functions. Testing Positive real functions, Testing driving point functions, Maximum modulus theorem, Properties of Hurwitz polynomials, Residue computations, Even & odd functions, Sturm's theorem. Driving Point Synthesis with L-C, R-C, R-L and R-L-C networks.

**Text books:**

1. A. Sudhakar & S. P. Shyammohan, Circuits and Networks, Tata McGraw Hill, thirteenth reprint, 2000.

2. William. H. Hayt, Jack E. Kemmerly & Steven M. Durbin, Engineering Circuit Analysis, McGraw Hill International, sixth edition, 2002.

3. Raymond A. DeCarlo & Pen-Min Lin, Linear Circuit Analysis, Oxford University Press, second edition, 2001.

4. M. E. Van Valkenburg, Introduction to Modern Network Synthesis, Wiley Eastern Ltd.

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Additional Reading:

2. Artice M. Davis, Linear Circuit Analysis, Thomson Asia Pte. Ltd., Singapore, first edition, 2001

3. M. E. Van Valkenburg, Network Analysis, Prentice Hall of India, third edition.

Termwork:

The termwork shall consist of atleast four laboratory experiments covering the whole of syllabus, duly recorded and graded as well as atleast four tutorial assignments, duly recorded and graded. This will carry a weightage of fifteen marks. A test shall be conducted and will carry a weightage of ten marks.

**[6]Applied Mathematics –III**

Lectures: 4 Hours / week

Paper: 100 Marks

Duration: 3 Hours

1. Laplace Transform:

1.1. Functions of bounded variation

Laplace transforms of 1, tn, eat, sinat, cosat, sinhat and coshat, erf(t) Linear Property of L.T. First shifting theorem, Second shifting theorem

L{tn f(t)}, L{f(t)/t}, L{∫ f(u)du}, L{dn/dt n f(t)}. Change of scale property of L.T. Unit step functions, Heaviside, Dirac delta functions, Periodic functions and their Laplace transforms.

1.2 Inverse Laplace Transforms

Evaluation of Inverse L.T, Partial fractions method ,Convolution theorem

1.3 Applications to solve initial and boundary value problems involving

ordinary diff. Equations with one dependent variable

2. Matrices(I)

2.1 Types of matrices, Adjoint of a matrix, Inverse of a matrix, Rank of Matrix, Linear dependence and independence of rows and columns of a matrix over a real field, Reduction to normal form and partitioning of a matrix.

2.2 Systems of Homogeneous and non-homogeneous equations, their consistency and solutions.

3. Complex Variables.

3.1 Functions of complex variables, Continuity and derivability of a function, Analytic functions, Necessary condition for f(z) to be analytic, sufficient condition (without proof),Cauchy-Riemann conditions in polar forms. Analytical and Milne-Thomson method to find analytic functions f (z)= u+ iv where (i) u is given (ii) v is given (iii) u+v (iv) u-v is given, Harmonic functions and orthogonal trajectories

3.2 Mapping

Conformal mapping, Bilinear mapping, Fixed points and standard transformation, inversion, reflection, rotation and magnification.

4. Fourier Series:

4.1 Orthogonality and orthonormal functions, Expression for a function in a series of orthogonal functions, Dirichlet's conditions, Fourier series of peroidic functions with period 2π and 2l

(Derivations of fourier coefficients ao, an, bn is not expected) Dirichlets Theorem Even and Odd functions. Half range sine and cosine expansions Parseval's Identities (without proof)

4.2 Complex form of Fourier Series

Fourier integral and fourier transform with properties in detail.

References:

1. P.N.Wartikar/J.N.Wartikar, Text book Applied Mathematics, Pune Vidyarthi Griha Prakashan, 1981.

2. Matrices Shantinarayan

3. Vector Analysis Murray R. Stiegel, Schaum Series.

**SEMESTER IV**

[1] Electrical Machines and Instruments

[1] Electrical Machines and Instruments

Lectures: 3 hours / week

Theory Paper: 3 hours and 100 marks

Practicals: 2 hours / week

Termwork: 25marks; Oral: 25 marks

Rationale

The subject Electrical Machines and Instruments familiarizes the student with concepts of construction and working of electrical measuring instruments. It discusses a few materials used in electrical engineering. Concepts of working of electrical motors widely used in industry are introduced.

Measuring Instruments

Principle of Permanent Magnet Moving Coil (PMMC), Moving Iron Instruments, Ammeters & Voltmeters, Operating Principles of the Electrodynamometer Instruments. Wattmeter, Energy meter, Electrostatic Instruments, Rectifier type Instruments, Extension of Ranges of Voltmeters and Ammeters. Principle of Power Factor & Frequency meter. Use of Current & Potential Transformers.

Measurement of R, L, and C

Measurement of low, medium & high resistances – Wheatstone & Kelvin bridge, Ohmmeter, Megger. A.C. bridge circuits for measurement of inductance & capacitance-Maxwell's, Hay's & Anderson's bridge, Schering bridge.

Potentiometers

Principles of D.C & A.C. Potentiometers & their applications.

Magnetic Properties of Materials

The magnetic dipole movement, diamagnetism. The origin of permanent magnetic dipoles in matter, Paramagnetism, Ferromagnetism.

D.C. Motors

Principles of working, E.M.F. equation, back – EMF, torque equations, methods of excitation, characteristics of D.C. shunt, series & compound motors, speed – torque characteristic of D.C. motors, starters, principles of speed control.

Three Phase Induction Motors

Rotating magnetic field, construction & principle of operation, slip, rotor frequency, development of equivalent circuit, torque equation, maximum torque, torque – speed characteristics, speed control. Starting methods, motor ratings.

Stepper Motor

Principle of working, characteristics & applications.

**Text Books:**

1. Sawhney A.K., A Course in Electrical & Electronic Measurements & Instrumentation, Dhanpatrai and Sons, 1993.

2. Golding, Electrical Measurements & Measuring Instruments, Wheeler Publishing, fifth edition, 1994.

3. Nagrath & Kothari, Electrical Machines, Tata McGraw Hill, second edition, 1997

4. Dekker A. J., Electrical Engineering Materials, Prentice Hall of India, twelfth reprint, 1987.

5. Srinivasan M. P., Stepping Motors, CEDT: Indian Institute of Science, 1985.

Termwork:

The termwork shall consist of atleast eight laboratory experiments covering the whole of syllabus, duly recorded and graded. This shall carry a weightage of fifteen marks. A test shall be conducted and will carry a weightage of ten marks.

**[2] Control Systems Engineering**

Lectures: 3 hours / week

Theory Paper: 3 hours and 100 marks

Practical: 2 hours / week

Term work: 25 marks, Oral: 25 marks.

Rationale

The subject Principles of control Systems is an introductory course in control system theory and practice. This course teaches conventional control systems, which would be useful in advanced courses in electronics, communication and signal processing.

Introduction to control system analysis

Introduction, examples of control systems, open loop control systems, closed loop control systems. Transfer function and impulse response of systems.

Control system components

DC and AC servomotors, servoamplifier, potientiometer, synchro transmitters, synchro receivers, synchro control transformer, stepper motors.

Mathematical modeling of systems

Importance of a mathematical model, Block diagrams, signal flow graphs, Masan's gain formula and its application to block diagram reduction.

Transient-Response Analysis

Impulse response function, First order system, second order system, time domain specifications of systems, analysis of transient-response using Second order model.

Steady – state Error Analysis

Classification of control systems according to "Type" of systems, Steady – state errors, static error constants, Steady – state analysis of different types of systems using step, ramp and parabolic input signals.

Stability Analysis

Introduction to concept of stability, Stability analysis using Routh's stability criterion, Absolute stability, Relative stability.

Root-Locus Analysis

Introduction, Root–Locus plots, summary of general rules for constructing Root–Locus, Root–Locus analysis of control systems.

Frequency-Response Analysis

Introduction, Frequency domain specifications, resonance peak and peak resonating frequency, relationship between time and frequency domain specification of systems.

Frequency-Response Plots

Bode plots, Polar plots, Log–magnitude Vs phase plots, Nyquist stability criterion, stability analysis, Relative stability, gain margin, phase margin, stability analysis of system using Bode plots.

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Closed-Loop Frequency Response

Constant gain and phase loci, Nichol's chart and their use in stability study of systems.

Controller Principles

Discontinuous controller modes, continuous controller modes, composite controllers.

**Textbooks:**

1. K. Ogata, Modern Control Engineering, Prentice Hall of India, third edition.

2. Benjamin C. Kuo, Automatic Control Systems, Prentice Hall of India, seventh edition.

3. Madan Gopal, Control Systems Principles and Design, Tata McGraw Hill, seventh edition, 1997.

Additional reading:

1. Curtis Johnson, Process Control Instrumentation Technology, Prentice Hall of India, fourth edition.

2. Paul Zbar, Industrial Electronics – A Text Lab Manual, Tata McGraw Hill, first edition, 1983.

Termwork:

The Termwork shall consist of at least ten experiments and assignments based on the whole syllabus, duly recorded and graded. This will carry a weightage of fifteen marks. A test shall be conducted and will carry a weightage of ten marks.

**[5]APPLIED MATHEMATICS -IV**

Lectures: 4 Hours / week

Paper: 100 Marks,

Duration: 3 Hours

1. Vector calculus & Analysis:

1.1 Scalar and vector point functions, Directional derivative, Curl and divergence, Conservative, Irrotational and solenoidal fields.

1.2 Line integral, Green's theorem for plane regions and properties of line integral, Stoke's theorem , Gauss's divergence theorem (with out proof) related identities and deductions.

2. Matrices(II):

2.1 Brief revision of vectors over real field , Inner product , Norm , Linear independence and orthogonality of vectors.

2.2 Characteristic polynomial , characteristic equation , characteristic roots and characteristic vectors of a square matrix, Properties of characteristic roots & vectors of different Types of matrices such as Orthogonal matrix, Hermitian matrix ,Skew –Hermitian matrix, Diagonable matrix, Cayley Hamilton's theorem(without proof), Functions of a square matrix, Minimal polynomial and Derogatory matrix.

2.3 Quadractic forms , congruent and orthogonal reduction of quadratic form, Rank, index ,signature and class value of quadratic form.

3. Complex variables:

3.1 Line integral of a function of complex variable.,Cauchy's theorem for analytic function (with proof), Cauchy's Goursat theorem (without proof), properties of Line integral,Cauchy's integral formula and deductions.

3.2 Singularities and poles:

Taylor's and Laurent's development (without proof) , Residue at isolated singularity and its evaluation.

3.3 Residue Theorem application to evaluate real integrals of type

o∫ 2π f(cosθ ,sinθ)dθ and ∝∫∝ f(x)dx.

References:

1. Complex Variable - Churchill, McGraw Hill, 2nd edition, 1960.

2. Theory of Function Complex Variable - Shantinarayanan, S. Chand & Co. , 1979.

3. Engineering Mathematics - S.S.Sastri, Prentice Hall of India, 2nd edition, 1989.

4. Element of Applied Mathematics - P.N.Wartikar/J.N.Wartikar, Pune Vidyarthi Griha Prakashan, 1981.