10MAT41 ENGINEERING MATHEMATICS - IV

Transcription

1 10MAT41 ENGINEERING MATHEMATICS - IV MVJCE 1 COURSE DIARY

2 SYLLABUS ENGINEERING MATHEMATICS IV Sub Code: 10MAT41 I A Marks: 25 Hours / Week: 4 Exam Hours:03 Total Hours: 52 Exam Marks: 100 PART-A Unit-I: NUMERICAL METHODS - 1 Numerical solution of ordinary differential equations of first order and first degree; Picard s method, Taylor s series method, modified Euler s method, Runge-kutta method of fourth-order. Milne s and Adams - Bashforth predictor and corrector methods (No derivations of formulae). [6 hours] Unit-II: NUMERICAL METHODS 2 Numerical solution of simultaneous first order ordinary differential equations: Picard s method, Runge-Kutta method of fourth-order. Numerical solution of second order ordinary differential equations: Picard s method, Runge-Kutta method and Milne s method. [6 hours] Unit-III: Complex variables 1 Function of a complex variable, Analytic functions-cauchy-riemann equations in cartesian and polar forms. Properties of analytic functions. Application to flow problems- complex potential, velocity potential, equipotential lines, stream functions, stream lines. [7 hours] Unit-IV: Complex variables 2 Conformal Transformations: Bilinear Transformations. Discussion of Transformations: 22, w=, (/) z wzewzaz ==+. Complex line integrals- Cauchy s theorem and Cauchy s integral formula. [7 hours] Unit-V: SPECIAL FUNCTIONS PART-B Solution of Laplace equation in cylindrical and spherical systems leading Bessel s and Legendre s differential equations, Series solution of Bessel s differential equation leading to Bessel function of first kind. Orthogonal property of Bessel functions. Series solution of Legendre s differential equation leading to Legendre polynomials, Rodrigue s formula. [7 hours] MVJCE 2 COURSE DIARY

3 Unit-VI: PROBABILITY THEORY - 1 Probability of an event, empherical and axiomatic definition, probability associated with set theory, addition law, conditional probability, multiplication law, Baye s theorem. [6 hours] Unit-VII: PROBABILITY THEORY- 2 Random variables (discrete and continuous), probability density function, cumulative density function. Probability distributions Binomial and Poisson distributions; Exponential and normal distributions. [7 hours] Unit-VIII: SAMPLING THEORY Sampling, Sampling distributions, standard error, test of hypothesis for means, confidence limits for means, student s t-distribution. Chi -Square distribution as a test of goodness of fit [6 hours] Text Books: 1. B.S. Grewal, Higher Engineering Mathematics, Latest edition, Khanna Publishers 2. Erwin Kreyszig, Advanced Engineering Mathematics, Latest edition, Wiley Publications. Reference Book: 1. B.V. Ramana, Higher Engineering Mathematics, Latest edition, Tata Mc. Graw Hill Publications. 2. Peter V. O Neil, Engineering Mathematics, CENGAGE Learning India Pvt Ltd.Publishers MVJCE 3 COURSE DIARY

4 LESSON PLAN 10MAT-41 Hours / Week: 05 I.A. Marks: 25 Total Hours: 60 No. of Topics Hrs Unit 1 Numerical Methods 1 Numerical solutions of first order and first degree ordinary differential equations 2 Taylor s series method 3 Modified Euler s method 4 Runge Kutta method of fourth order 5 Milne s and Adams-Bashforth predictor 6 corrector methods Unit 2 Complex Variables 7 Function of a complex variable, Limit, Continuity Differentiability-Definitions 8 Analytic functions 9 Cauchy Riemann equations in Cartesian and polar forms 10 Properties of analytic functions 11 Conformal Transformation Definition 12 Discussion of transformations: W = z 2, W = e z, W = z + (1/z), z 0 13 Bilinear transformations Unit 3 Complex Integration 14 Complex line integrals 15 Cauchy s theorem 16 Cauchy s integral formula 17 Taylor s and Laurent s series (Statements only) 18 Singularities, Poles, Residues 19 Cauchy s residue theorem Unit 4 Series solution of Ordinary Differential Equations and Special Functions 20 Series solution 21 Frobenius method 22 Series solution of Bessel s D.E. leading to Bessel function of first kind 23 Equations reducible to essel s D.E 24 series solution of Legendre s D.E 25 leading to Legendre polynomials 26 Rodirgue s formula Unit 5 Statistical Methods 27 Curve fitting by the method of least squares: y = a + bx 28 y = a + bx+cx 2, y = ax b, y = ab x, y = ae bx 29 Correlation and Regression 30 Probability: Addition rule, Conditional probability 31 Multiplication rule 32 Baye s theorem Unit 6 33 Random Variables (Discrete and Continuous) 34 p.d.f 35 c.d.f MVJCE 4 COURSE DIARY

5 No. of Hrs Topics 36 Binomial 37 Poisson 38 Normal 39 Exponential distributions Unit 7 40 Sampling 41 Sampling distribution 42 Standard error 43 Testing of hypothesis for means 44 Confidence limits for means 45 Student s t distribution 46 Chi-square distribution as a test of goodness of fit Unit 8 47 Concept of joint probability Joint probability distribution 48 Discrete and Independent random variables 49 Expectation, Covariance, Correlation coefficient 50 Probability vectors, Stochastic matrices, Fixed points, Regular stochastic matrices 51 Markov chains, Higher transition probabilities 52 Stationary distribution of regular Markov chains MVJCE 5 COURSE DIARY

6 10EES42 MICROCONTROLLERS MVJCE 6 COURSE DIARY

7 SYLLABUS SUBJECT CODE: 10ES42 IA MARKS: 25 SUBJECT: MICROCONTROLLERS EXAM HOURS: 3 (Common to, EE, EC, IT, TC, BM and ML) EXAM MARKS: 100 HOURS / WEEK: 04 TOTAL HOURS: 52 UNIT 1: Microprocessors and microcontroller. Introduction, Microprocessors and Microcontrollers, RISC & CISC CPU Architectures, Harvard & Von-Neumann CPU architecture, Computer software. The 8051 Architecture: Introduction, Architecture of 8051, Pin diagram of 8051, Memory organization, External Memory interfacing, Stacks. 6 Hours UNIT 2: Addressing Modes: Introduction, Instruction syntax, Data types, Subroutines, Addressing modes: Immediate addressing, Register addressing, Direct addressing, Indirect addressing, relative addressing, Absolute addressing, Long addressing, Indexed addressing, Bit inherent addressing, bit direct addressing. Instruction set: Instruction timings, 8051 instructions: Data transfer instructions, Arithmetic instructions, Logical instructions, Branch instructions, Subroutine instructions, Bit manipulation instruction. 6 Hours UNIT 3: 8051 programming: Assembler directives, Assembly language programs and Time delay calculations. 6 Hours UNIT 4: 8051 Interfacing and Applications: Basics of I/O concepts, I/O Port Operation, Interfacing 8051 to LCD, Keyboard, parallel and serial ADC, DAC, Stepper motor interfacing and DC motor interfacing and programming 7 Hours UNIT 5: 8051 Interrupts and Timers/counters: Basics of interrupts, 8051 interrupt structure, Timers and Counters, 8051 timers/counters, programming 8051 timers in assembly and C. 6 Hours UNIT 6: 8051 Serial Communication: Data communication, Basics of Serial Data Communication, 8051 Serial Communication, connections to RS-232, Serial communication Programming in assembly and C. 8255A Programmable Peripheral Interface:, Architecture of 8255A, I/O addressing,, I/O devices interfacing with 8051 using 8255A. 6 Hours Course Aim The MSP430 microcontroller is ideally suited for development of low-power embedded systems that must run on batteries for many years. There are also applications where MSP430 microcontroller must operate on energy harvested from the environment. This is possible due to the ultra-low power operation of MSP430 and the fact that it provides a complete system solution including a RISC CPU, flash memory, on-chip data converters and on-chip peripherals. MVJCE 7 COURSE DIARY

8 UNIT 7: Motivation for MSP430microcontrollers Low Power embedded systems, On-chip peripherals (analog and digital), low-power RF capabilities. Target applications (Single-chip, low cost, low power, high performance system design). 2 Hours MSP430 RISC CPU architecture, Compiler-friendly features, Instruction set, Clock system, Memory subsystem. Key differentiating factors between different MSP430 families. 2 Hours Introduction to Code Composer Studio (CCS v4). Understanding how to use CCS for Assembly, C, Assembly+C projects for MSP430 microcontrollers. Interrupt programming. 3 Hours Digital I/O I/O ports programming using C and assembly, Understanding the muxing scheme of the MSP430 pins. 2 Hours UNIT 8: On-chip peripherals. Watchdog Timer, Comparator, Op-Amp, Basic Timer, Real Time Clock (RTC), ADC, DAC, SD16, LCD, DMA. 2 Hours Using the Low-power features of MSP430. Clock system, low-power modes, Clock request feature, Low-power programming and Interrupt. 2 Hours Interfacing LED, LCD, External memory. Seven segment LED modules interfacing. Example Realtime clock. 2 Hours Case Studies of applications of MSP430 - Data acquisition system, Wired Sensor network, Wireless sensor network with Chipcon RF interfaces. 3 Hours TEXT BOOKS: 1. The 8051 Microcontroller and Embedded Systems using assembly and C -, Muhammad Ali Mazidi and Janice Gillespie Mazidi and Rollin D. McKinlay; PHI, 2006 / Pearson, MSP430 Microcontroller Basics, John Davies, Elsevier, 2010 (Indian edition available) REFERENCE BOOKS: 1. The 8051 Microcontroller Architecture, Programming & Applications, 2e Kenneth J. Ayala ;, Penram International, 1996 / Thomson Learning The 8051 Microcontroller, V.Udayashankar and MalikarjunaSwamy, TMH, MSP430 Teaching CD-ROM, Texas Instruments, 2008 (can be requested ) 4. Microcontrollers: Architecture, Programming, Interfacing and System Design,Raj Kamal, Pearson Education, 2005 MVJCE 8 COURSE DIARY

9 LESSON PLAN SUBJECT CODE: 10ES42 IA MARKS: 25 SUBJECT: MICROCONTROLLERS EXAM HOURS: 03 EXAM MARKS: 100 TOTAL HOURS: 60 Chapter No. 1 Chapter name Hrs Topic to be covered Microprocessors And Microcontroller 1 Introduction, Microprocessors and Microcontrollers, A Microprocessors survey. 2 RISC & CISC CPU Architectures, Harvard & Von-Neumann CPU architecture. 3 Introduction, 8051 Microcontroller Hardware 4 Input / Output Pins 5 Ports and Circuits External Memory, Counter and Timers 6 Serial Data Input / Output, Addressing Modes and Operations Jump and Call Instructions 8051 programming in C 7 Interrupts. types 8 Introduction, Addressing modes, External data Moves 9 Code Memory, Read Only Data Moves / Indexed Addressing mode 10 PUSH and POP Opcodes, Data exchanges, Example Programs 11 Byte level logical Operations, Bit level Logical Operations 12 Rotate and Swap Operations, Example Programs 13 Arithmetic Operations: Flags, Incrementing and Decrementing, Addition, Subtraction 14 Multiplication and Division, Decimal Arithmetic, 15 Example Programs. 16 The JUMP and CALL Program range 17 Jumps, calls programs 18 Subroutines programs 19 Interrupts and Returns 20 More Detail on Interrupts 21 Example Problems 22 Example Problems 23 Data types and time delays in 8051C 24 I/O programming 25 Data conversion programs 26 Accessing code ROM space, 27 Communication Programs in C 28 logic operations 29 data serialization 30 Example programs MVJCE 9 COURSE DIARY

10 Chapter No. Chapter name Hrs Topic to be covered 5. Timer / Counter Programming in Programming 8051 Timers 32 Programming 8051 Timers (cont.) 33 Counter Programming 34 Counter Programming (cont.) 35 Programming timers 0 and 1 in 8051 C 36 Programming timers 0 and 1 in 8051 C (cont.) 37 Example programs 38 Basics of Serial Communication connections to RS Serial Communication Serial communication Programming 41 Programming the second serial port 42 Serial port programming in C 43 Example Programs 44 Exercise programs Interrupts 46 Programming Timer Interrupts 7 Interrupts Programming 47 Programming External Hardware Interrupts 48 Programming the Serial Communication Interrupts 49 Interrupt Priority in the 8051/52 50 Interrupt programming in C 51 Exercise and example programs 52 Interfacing 8051 to LCD 53 Interfacing 8051 to Keyboard 54 Interfacing 8051 to parallel and serial ADC Interfacing and Applications 55 Interfacing 8051 to DAC 56 Interfacing 8051 to Stepper motor interfacing 57 Interfacing 8051 to DC motor interfacing 58 Interfacing 8051 to PWM 59 Solving of VTU Question Paper 60 Solving of VTU Question Paper MVJCE 10 COURSE DIARY

11 10ES43 CONTROL SYSTEMS MVJCE 11 COURSE DIARY

12 SYLLABUS SUBJECT CODE: 10ES43 IA MARKS: 25 SUBJECT: CONTROL SYSTEMS EXAM HOURS: 3 (Common to, EE, EC, IT, TC, BM and ML) EXAM MARKS: 100 HOURS / WEEK: 04 TOTAL HOURS: 52 PART A UNIT 1: Modeling of Systems: Introduction to Control Systems, Types of control systems, Effect of feedback systems, Differential equations of physical systems Mechanical systems- Friction, Translational systems (Mechanical accelerometer, Levered systems excluded), Rotational systems, Gear trains. Electrical systems, Analogous systems. 6 Hours UNIT 2: Block diagrams and signal flow graphs: Transfer functions, Block diagrams, Signal Flow graphs (State variable formulation excluded). 7 Hours UNIT 3: Time Response of feed back control systems: Standard test signals, Unit step response of First and second order systems, Time response specifications, Time response specifications of second order systems, steady state errors and error constants. 7Hours UNIT 4: Stability analysis: Concepts of stability, Necessary conditions for Stability, Routh-Hurwitz stability criterion, Relative stability analysis; Special cases of RH criterion. 6 Hours PART B UNIT 5: Root Locus Techniques: Introduction, basic properties of root loci, Construction of root loci. 6 Hours UNIT 6: Stability analysis in frequency domain: Introduction, Mathematical preliminaries, Nyquist Stability criterion, (Inverse polar plots excluded), Assessment of relative stability using Nyquist criterion, (Systems with transportation lag excluded). 7Hours UNIT 7: Frequency domain analysis: Correlation between time and frequency response, Bode plots, All pass and minimum phase systems, Experimental determination of transfer functions, Assessment of relative stability using Bode Plots. 7 Hours UNIT 8: Introduction to State variable analysis: Concepts of state, state variable and state models for electrical systems, Solution of state equations. 6 Hours MVJCE 12 COURSE DIARY

13 TEXT BOOK : 1. Control Systems Engineering, I. J. Nagarath and M.Gopal, New Age International (P) Limited, 4th Edition Modern Control Engineering, K. Ogata, PHI, 5th Edition, REFERENCE BOOKS: 1. Control Systems Engineering,Norman S Nise,Wiley Student Edition,5th Edition, Automatic Control Systems, Benjamin C.Kuo and Farid Golnaaghi, Wiley Student Edition,8th Edition, Feedback and Control Systems,Joseph J Distefano III and other, Schaum s Outlines,TMH,2nd Edition, Control Systems, Ananda Kumar, PHI,2009. MVJCE 13 COURSE DIARY

14 LESSON PLAN SEMESTER: IV TEACHING HOURS: 60 SUB: CONTROL SYSTEMS SUB_CODE: 10ES43 Chapter No Chapter name Modeling of systems Block diagrams and signal flow graphs Time response of feedback control systems Hrs Topic to be covered 1 Introduction to overall subject, Question paper pattern Discussion of types of control system 2 Introduction to Mathematical modeling of system, dynamic equation, F-V, F-I analysis 3 Problems on Translational system 4 Problems on Translational system 5 Introduction to rotational system, T-V & T-I analysis & Problems on rotational system 6 Introduction to modeling of gear system 7 Solution of numericals on gear system 8 Introduction to transfer functions, derivation of transfer functions of physical systems 9 Derivation of transfer functions of physical systems (contd.)& solution of numerical 10 Introduction to block diagram & construction of block diagram; introduction to poles & zeroes 11 Introduction to signal flow graph, construction of signal flow graph & Mason s gain formula 12 Problems on block diagram reduction technique & signal flow graph 13 Problems on block diagram reduction technique & signal flow graph 14 Problems on signal flow graph 15 Problems on multiple input & multiple output systems 15 Introduction to time response analysis & standard input signals 16 Time response analysis of first order system applying unit (i) Step, (ii) Ramp, (iii) Impulse & (iv) Sinusoidal inputs 17 Solution of numericals on Time response analysis of first order system 18 Time response analysis of second order system Analysis of Time Response (i) Overshoot & Undershoot, (ii) 19 Underdamped, Overdamped & Critically Damped systems, (iii) Settling time 21 Time domain specifications & derivation of expressions for them 22 Solution of numericals on second order system & Time domain specifications 23 Introduction to static error coefficient & problems on finding static error coefficient MVJCE 14 COURSE DIARY

15 Chapter No Chapter name Stability analysis Root Locus Technique Stability in the Frequency domain Frequency domain analysis Hrs Topic to be covered 24 Introduction to stability analysis, concept of stability and role of poles & zeroes on stability 25 Techniques of stability analysis : Time domain & Frequency domain; introduction to Routh-Hurwitz criterion 26 Necessary & sufficient conditions of stability as per Routh-Hurwitz criterion and formation of Routh s Table 27 Concept of Relative Stability & its analysis 28 Solution of numericals on stability analysis applying Routh-Hurwitz criterion 29 Solution of numericals on stability analysis applying Routh-Hurwitz criterion when zero appears on first column 30 Solution of numericals on stability analysis 31 Introduction to Root Locus diagram & procedure to plot the Root Locus diagram 32 Procedure to plot the Root Locus diagram (contd.) 33 Solution of numericals on Root Locus 34 Solution of numericals on Root Locus 35 Solution of numericals on Root Locus 36 Solution of numericals on Root Locus 37 Solution of numericals on Root Locus 38 Introduction to concept of polar plot 39 Concept of encircle & enclose 40 Introduction to concept of Nyquist plot criterion ; construction of GH- Plot 41 Assessment of stability from GH Plot & solution of mu,ericals 42 Introduction to assessment of relative stability using Nyquist criterion 43 Solution of numericals on Nyquist plot 44 Solution of numericals on Nyquist plot 45 Solution of numericals on Nyquist plot 46 Introduction to frequency domain analysis & discussion of advantages of frequency response analysis 47 Discussion of frequency domain specifications & derivation of expressions for them 48 Introduction to phase margin & gain margin & correlation between time domain & frequency domain 49 Introduction to Bode plot 50 Problems on Bode plot 51 Determination of Gain Margin & Phase Margin from Bode Plot 52 Assessment of stability from Bode Plot 53 Solution of numericals on Bode plot 54 Solution of numericals on Bode plot MVJCE 15 COURSE DIARY

16 Chapter No. 8. Chapter name Introduction to state variable analysis Hrs Topic to be covered 55 Introduction to concepts of state & state variables, Advantages of state space analysis 56 Introduction to state space representation & state space representation of physical systems 57 Discussion of state space representation of Electrical network 58 Problems on state space representation of Electrical network 59 Introduction to state transition matrix & problems on state system matrix 60 Problems on solution of state equations MVJCE 16 COURSE DIARY

17 MODEL QUESTION PAPER I 1. Distinguish between Open-Loop and Closed-Loop control system. (4) 2. A system has 30% overshoot and settling time of 5 seconds for an unit step input. Determine (i) The transfer function (ii) Peak time (t p ) (iii) Output response (Assume e ss as 2%) (8) 3. Distinguish between type of system and Order of the system. Determine the steady state errors for Type 1 and Type 2 systems with the inputs (i) Unit Step (ii) Unit Parabolic. (6) 4. The open loop transfer function of a unity feedback system is given by G(s) = K (s + 2) (s + 4) (s 2 + 6s + 25) Discuss the stability of the system. (8) 5. Negative non-unity feedback system is represented by G(s) = 100(s + 5) H(s) = 1/s (s 2 + 5s + 10) Determine (i) Order and Type of the system and (ii) Steady state error for unit ramp input. (10) 6. Determine the stability of the control system whose characteristic equations are given by (i) s 6 + 2s 5 + 8s s s s + 16 = 0 (ii) s s s s + 80 = 0 (12) 7. Explain the terms Gain Margin and Phase Margin of the system. (6) 8. By means of the Nyquist criterion, determine whether the closed loop system having the following open-loop transfer function is stable or not. If not, how many closed loop poles lie in the right half S-plane? (14) G(s) H(s) = 1 + 4s s 2 + (1 + s) (1 + 2s) MVJCE 17 COURSE DIARY

18 MODEL QUESTION PAPER II 1. Derive an expression for the response of a second-order system excited by unit step input. (8) 2. The open-loop transfer function of a unity feedback servomotor system is given by G(s) = 1.6 ( s) ( s) Calculate (i) Damping ratio (ii) Percentage overshoot (iii) Damped frequency of oscillations. Assuming the input to be unit step and also find the study state error. (10) 3. The Open Loop transfer function of a control system is given by G(s) H(s) = K s (s + 2) (s + 10) Draw the Bode Plots for K = 10, and determine the stability of the system. Also determine the value of K so that the system may be stable with (i) Gain Margin equal to 6db. (ii) Phase Margin equal to 45 0 (16) 4. A unity feedback has G(s) = 40 (s + 2) s (s + 1) (s + 4) Determine (i) Type of the system (ii) Error coefficients Kp, Kv, Ka (iii) Steady-State Error for the input r(t) = 4(t) (6) 5.Write short notes on any four of the following (4 Χ 5 = 20) i. Servo mechanisms ii. Automatic regulating systems iii. Speed control system iv. M and N circles v. Stability of non-linear systems vi. Describing function method. 6.The open loop transfer function of a certain system is given by G(s) H(s) = K s (s + 4) (s 2 + 4s + 20) (10) Sketch the Root Locus. 7. (a) Derive the Frequency response specifications for a second order system (b) State construction rules of Root Locus. 8. (a). Sketch the Nyquist plot of the following G(s) = K (s + 2) (s 2 + 3s + 1) (12) (8) (20) MVJCE 18 COURSE DIARY

19 10EE44 FIELD THEORY MVJCE 19 COURSE DIARY

20 SYLLABUS SUBJECT CODE: 10ES44 IA MARKS: 25 SUBJECT:FIELD THEORY EXAM HOURS: 3 EXAM MARKS: 100 HOURS / WEEK: 04 TOTAL HOURS: 52 PART A UNIT -1 a. Coulomb s Law and electric field intensity: Experimental law of Coulomb, Electric field intensity, Field due to continuous volume charge distribution, Field of a line charge. 03 Hours b. Electric flux density, Gauss law and divergence: Electric flux density, Gauss law, Divergence, Maxwell s First equation (Electrostatics), vector operator and divergence theorem 04 Hours UNIT- 2 a. Energy and potential: Energy expended in moving a point charge in an electric field, The line integral, Definition of potential difference and Potential, The potential field of a point charge and system of charges, Potential gradient, Energy density in an electrostatic field 04 Hours b. Conductors, dielectrics and capacitance: Current and current density, continuity of current, metallic conductors, conductor properties and boundary conditions, boundary conditions for perfect dielectrics, capacitance and examples. 03 Hours UNIT- 3 Poisson s and Laplace s equations: Derivations of Poisson s and Laplace s Equations, Uniqueness theorem, Examples of the solutions of Laplace s and Poisson s equations. 06 Hours UNIT -4 The steady magnetic field: Biot-Savart law, Ampere s circuital law, Curl, Stokes theorem, magnetic flux and flux density, scalar and Vector magnetic potentials. 06 Hours PART B UNIT- 5 a. Magnetic forces: Force on a moving charge and differential current element, Force between differential current elements, Force and torque on a closed circuit. 03 Hours b. Magnetic materials and inductance: Magnetization and permeability, Magnetic boundary conditions, Magnetic circuit, Potential energy and forces on magnetic materials, Inductance and Mutual Inductance. 04 Hours UNIT-6 Time varying fields and Maxwell s equations: Faraday s law, displacement current, Maxwell s equation in point and Integral form, retarded potentials. 06 Hours UNIT- 7 Uniform plane wave: Wave propagation in free space and dielectrics, Poynting s theorem and wave power, propagation in good conductors, skin effect. 07 Hours UNIT- 8 Plane waves at boundaries and in dispersive media: Reflection of uniform plane waves at normal incidence, SWR, Plane wave propagation in general directions. 06 Hours MVJCE 20 COURSE DIARY

21 TEXT BOOK: 1. Engineering Electromagnetics, William H Hayt Jr. and John A Buck, Tata McGraw-Hill, 7th edition, Principles of Electromagnetics, Matthew N.O. Sadiku, 4th Edition, Oxford University Press, REFERENCE BOOKS: 1.Electromagnetics with Applications, John Krauss and Daniel A Fleisch, McGraw-Hill, 5th edition, Electromagnetism-Theory and Applications, Ashutosh Pramanik, PHI, 2nd edition,reprint Field and Wave Electromagnetics, David K Cheng, Pearson Education Asia, 2nd edition, , Indian Reprint MVJCE 21 COURSE DIARY

22 Unit No. 1a. 1b. 2a. 2b. SEMESTER: IV (NS) TEACHING HOURS: 60 LESSON PLAN SUB: FIELD THEORY SUB_CODE: 10ES44 Unit Name Hrs Topic to be covered Coulomb s Law and electric field intensity Electric flux density, Gauss law and divergence Energy and potential Conductors, dielectrics and capacitance 1 Introduction to vectors 2 Review of vectors continued 3 Explanation of coulomb s law & problems 4 Problems on Coulomb s law continued 5 Definition of electrical field intensity and explanation same 6 Problems on E.F.I 7 Problems on E.F.I continued 8 Problems on E.F.I continued 9 General representation of E.F.I for various types of charges to be discussed 10 Derivation for E.F.I at any point due to infinite lint charge 11 Derivation for E.F.I for finite line charge and sheet charge to find electrical field intensity 12 Problems on line charge, surface charge to find electrical field intensity 13 Finding electrical field intensity for ring & disc charge 14 Derivation for work done in an electrical field in moving charge 15 Solved problems in electrical field in moving charge 16 Statement & Proof of Gauss Law& Its Application 17 Problem & Application on Gauss Law 18 Statement & Proof of Gauss Law in Point form,laplace, Poission s Equation 19 Problems on Gauss Law 20 Problems on gauss laws 21 Electric Scalar Potential, Differential Relation 22 Problems & Differential Relation 23 Problem on Potential & Work Done 24 Problem on Potential, 25 Definition of electric Flux 26 Current, Current Density Relation B/w J & Velocity, Continuity Eqn.,Metallic Conductors, Introduction to Boundary Conditions 27 Energy Density & Electric Field 28 Capacitance, Composite Capacitance 29 Energy & Energy Density for a Capacitor 30 Problem Based on Capacitance MVJCE 22 COURSE DIARY

23 Unit No a. 5b Unit Name Hrs Topic to be covered Poisson s and Laplace s The steady magnetic field Magnetic forces Magnetic materials & inductance Time varying fields and Maxwell s equations Uniform plane wave Plane waves at boundaries and in dispersive media 31 Problems on Divergence, Laplace, Poission s Equation 32 Problems on Laplace, Poission s Equation 33 Problems on Laplace, 34 Poission s Equation to be continued 35 Explanation of Biot Savart Law, Relation B/w B & H and B for ifinite line conductor 36 B for finite Line Conductor, Ampere s Law in Integral & Differential form 37 Problems on Ampere s Law 38 Define of curl, stokes Theorem, Scalar Magnetic Potential 39 Vector Magnetic Potential Problem 40 Vector Magnetic Potential Problem continued 41 Force on Moving Charge & Different Current Element, B/w Different Current Element 42 Force & Torque on Closed Circuit, Magnetization & Permeability Problems 43 Boundary condition & Problems 44 Magnetic circuit, Energy & forces on magnetic materials, self inductance 45 Faraday s Law & Displacement Current Problem 46 Maxwell s Eqn. In Point & Integral Form 47 Retarded Potential, Problems 48 Related problems continued 49 Wave Propagation in Force space & Dielectric Problems 50 Pointing Vector Power Consideration 51 Problems on Pointing Vector 52 Plane Wave at Boundaries 53 Problems on Plane Waves 54 Problems continued 55 Problems on plane waves 56 Reflection of Uniform Plane Wave at Normal Incidence 57 Problems on Reflection of Uniform Plane Wave at Normal Incidence 58 Skin Depth, Problems on Skin Depth, For Power Dielectric 59 Standing Wave Ratio on a Transmission Line 60 Problems on Standing Wave MVJCE 23 COURSE DIARY

24 MODEL QUESTION PAPER 1.a. Find the expression of the field component at a far point due to a dipole. 06 b. Find the far field for the linear quadruple having three charges along Z-axis.2q at Z=0,-q at Z=a and q at Z=a. 07 c. E= 10 [xa x +ya y ]-2a z V/m x 2 +y 2 Potential at (3,4,5) is 10 volt. Find V at (6, -8,7) a. State and prove Gauss s law and determine the field due to an infinite line charge using this. 10 b. A spherical volume charge density is given by ρ= ρ o (1-r 2 /a 2 ) r a r>a I. Calculate the total charge Q ii. Find the electric field intensity E outside the charge distribution iii. Find the electric field intensity for r a. iv. Show that the maximum value of E is at r= 0.745a 10 3.a. Derive Expressions for energy and energy density in a capacitor 06 b. Show that the capacitance between two identical spheres of radius R separated by a distance (d >>R) is given by 4πε o dr/ 2(d-R) 08 c. Derive the expression for the magnetic flux density at a point due to an infinitely long current carrying conductor a. State and explain the Amperes circuit law. Apply the law to determine the magnetic field inside and outside a conductor of radius a. The conductor carries a current of I amperes. Sketch the fields. 06 b. Determine the magnetic vector potential near a long conductor 0f carrying steady current. 06 c. Calculate the displacement current when AC voltage of 100sin(2π10 4 t) is applied across a capacitor of 4 microfarad at instances0.01ms, 1.0ms a. How many turns are required for a square loop of 100 mm on a side to develop a maximum emf of 10 mv RMS if the loop rotates at 30 r/s in earth s magnetic field? Take B = 60 micro sec 10 b. Show that the line integral of magnetic vector potential vector A over a closed loop gives the magnetic flux passing through the area bounded by the loop a. Prove wave propagation in a general medium & arrive at wave propagation in a good conducing medium. 10 b. Determine Attenuation constant, Phase shift constant, Phase velocity & intrinsic impedance of the medium a. State and prove Poynting theorem. 08 b. Prove wave propagation in a general medium & arrive at wave propagation in a good conducting medium a. Explain polarization of plane waves. Write different types of polarization of plane wave. 10 MVJCE 24 COURSE DIARY

25 b. Define wave & uniform plane wave W.R.T Circular & Elliptical polarization of electric field a. What is Equi-potential surface? Give two examples of such surfaces. 10 b. Derive an expression for skin depth. Give an example for it Write short note on i. Wave Propagation in a good conducting medium ii. Brewster angle iii. Linear polarization iv. Boundary condition between two dielectrics (5Marks each) MVJCE 25 COURSE DIARY

26 10EE45 POWER ELECTRONICS MVJCE 26 COURSE DIARY

27 SYLLABUS SUBJECT CODE: 10EE45 IA MARKS: 25 SUBJECT: POWER ELECTRONICS EXAM HOURS: 3 EXAM MARKS: 100 HOURS / WEEK: 04 TOTAL HOURS: 52 PART A UNIT 1: Power Semiconductor Devices: Introduction to semiconductors, Power Electronics, Power semiconductor devices, Control Characteristics. Types of power electronic converters and industrial applications-drives, Electrolysis, Heating, Welding, Static Compensators, SMPS, HVDC power transmission, Thyristorized tap changers and Circuit breakers. 7 hours UNIT 2: Power Transistors: Power BJT s switching characteristics, switching limits, base drive control. Power MOSFET s and IGBT s characteristics, gate drive, di/dt and dv/dt limitations. Isolation of gate and base drives. Simple design of gate and base drives. 6 Hours UNIT 3: Thyristors Introduction, Two Transistor Model, characteristics-static and dynamic. di/dt and dv/dt protection. Ratings of thyristors. Thyristor types. Series and parallel operation of Thyristors. Thyristor firing circuits. Design of firing circuits using UJT, R, R-C circuits. Analysis of firing circuits using operational amplifiers and digital IC s. 7 Hours UNIT 4: Commutation Techniques: Introduction. Natural Commutation. Forced commutation- selfcommutation, impulse commutation, resonant pulse commutation and complementary commutation. 6 Hours PART B UNIT 5: Controlled Rectifiers: Introduction. Principle of phase controlled converter operation. Single- phase semi-converters. Full converters. Three-phase half-wave converters. Three-phase full-wave converters. 7 Hours UNIT 6: Choppers: Introduction. Principle of step-down and step-up chopper with R-L load. Performance parameters. Chopper classification. Analysis of impulse commutated thyristor chopper (only qualitative analysis) 6 Hours UNIT 7: Inverters: Introduction. Principle of operation. Performance parameters. Single-phase bridge inverters. Threephase inverters. Voltage control of single-phase inverters single pulse width, multiple pulse width, and sinusoidal pulse width modulation. Current source inverters. 7 Hours MVJCE 27 COURSE DIARY

28 UNIT 8: (a) AC Voltage Controllers: Introduction. Principle of ON-OFF and phase control. Single-phase, bidirectional controllers with resistive and R-L loads. (b) Electromagnetic Compatibility: Introduction, effect of power electronic converters and remedial measures. 6 Hours Text Book: 1. Power Electronics, M.H.Rashid,, Pearson, 3 rd Edition, Power Electronics, M.D. Singh and Khanchandani K.B., T.M.H., 2 nd Edition, 2001 References: 1.Power Electronics Essentials and Applications,L.Umanand, Wiley India Pvt Ltd,Reprint, Thyristorised Power Controllers, G.K. Dubey, S.R. Doradla, A. Joshi and R.M.K. Sinha, New Age International Publishers. 3. Power Electronics Converters, Applications and Design, Ned Mohan, Tore M. Undeland, and William P. Robins, Third Edition, John Wiley and Sons, Power Electronics: A Simplified Approach, R.S. Ananda Murthy and V. Nattarasu, pearson/sanguine Technical Publishers. MVJCE 28 COURSE DIARY

29 LESSON PLAN SUBJECT CODE: 10EE45 IA MARKS: 25 SUBJECT: POWER ELECTRONICS (For EE Only) EXAM HOURS: 3 TOTAL HOURS: 60 Chapter No 1 2 Chapter Introduction to power semiconductor devices Power transisters 3 Thyristors 5 AC voltage controllers Hour No. 01 Topics To Be Covered Applications of power electronics, history of power electronics 02 Power semiconductors devices 03 Control characteristics of power devices, 04 Types of power electronics circuits 05 Thyristorized power controllers, classification & characteristics 06 Peripheral effects of different devices 07 Power BJT s, switching characteristics 08 switching limits, base-drive control 09 Power MOSFETs, switching characteristics 10 gate drive. IGBT s, 11 di/dt and dv/dt limitations 12 Isolation of gate and base drives 13 Design of gate and base drive 14 Dynamic characteristics of Thyristor 15 Two transistor model of Thyristor 16 Thyristor turn ON and Thyristor turn OFF 17 di/dt and dv/dt ptotection, Thyristor types 18 series and parallel operation of thyristors 19 Thyristor firing circuits 20 Design of firing circuits using UJT, op-amps, and digital IC s 21 Introduction to AC voltage controllers 22 Principles of ON & OFF control 23 Principles of phase control 24 Single-phase Bi-Directional controllers with resistive loads. 25 Single-phase controllers with inductive loads 26 problems MVJCE 29 COURSE DIARY

30 Chapter No 6 Chapter Controlled rectifiers 7 DC Choppers 8 Inverters 4 Commutation techniques Hour No. Topics To Be Covered 27 Introduction to rectifiers Principles of phase controlled converter operation 28 Single phase semi converters with R load 29 Single phase semi converters with RL load 30 Single phase full converters - with R load 31 Single phase full converters - with RL load 32 Continuous and discontinuous conduction 33 Three phase half wave converters 34 Three phase semi converters 35 Three phase full converters 36 Problems 37 Introduction to Choppers. 38 Principle of step-down 39 step-up choppers 40 step-down chopper with RL loads 41 Performance parameters 42 Chopper classification of Choppers. 43 Analysis of Impulse commutated thyristor chopper (only qualitative analysis) 44 Solutions to Problems. 45 Introduction to Inverters. 46 Principle of operation of Inverters. 47 performance parameters 48 single phase bridge inverters 49 Three phase inverters 50 Voltage control of single phase inverters- single pulse, multiple pulse modulation 51 sinusoidal pulse width modulation 52 current source inverter 53 variable DC link inverter 54 problems 55 Introduction to Thyristor commutation techniques - Natural commutation - Forced commutation 56 Self commutation, Impulse commutation 57 Resonant pulse commutation, Complimentary commutation 58 External pulse commutation, 59 Line side commutation 60 Load side commutation MVJCE 30 COURSE DIARY

31 POWER ELECTRONICS (06EE45) Model Question Paper-I Duration: 3 Hrs Max. Marks: 100 Answer any five questions 1. a) Discuss the VI characteristics of the Triac. Compare the characteristics of SCR with Triac. b) List the classifications of power controllers. Mention at least two applications of each. 06 c) For A snubber circuit The junction capacitance of thyristor is C j2 = 15 pf and can be assumed to be independent of the off state voltage. The limiting value of charging current to turn an thyristor is 5mA and the critical value is 200V/µs. Determine the value of capacitance C s so that the thyristor will not be turned on due to dv/dt a) Give simple circuit configuration for providing over voltage and over current protection for SCR s. 10 b) Design the triggering circuit the parameters of the UJT are V BB = 20V, η=0.66, I p = 10µA, V v = 2.5 V, and I v = 10mA. The frequency of oscillation is f = 1KHz and the width of the gate is t g = 40µs a) Explain briefly the operation of a 3-phase dual converter. 10 b) A single phase full converter has an R-L load of L = 8mH, R = 5Ω and E = 10V. The input voltage is 120V rms at 60Hz for a delay angle of α=60. Find (i) Load current (ii) The Fourier series for the input current (iii) Displacement factor input power factor a) With the help of neat diagram explain the operation of a single phase semi converter with R-L load. b) A three phase half-wave converter is operated from a three phase Y connected 20V, 60Hz. Supply and the load resistance is R = 10Ω. If it is required to obtain an average output voltage of 50% of the maximum possible output voltage, calculate (a) The delay angle α (b) the rms and average output currents. (c) The transformer utilization factor TUF (d) The input power factor PF. 5. a)distinguish clearly between natural commutation and forced commutation. b) Explain the principle of operation of an impulse commutation circuit. c) In a self commutation circuit the initial capacitor voltage V 0 = 600V, capacitance C = 40µF and inductance L = 10µH. Determine the peak value of resonant current and conduction time of thyristor MVJCE 31 COURSE DIARY

32 6. a) With relevant waveform explain the working of single phase full-wave controller connected to a resistive load. Derived the expression for rms output voltage. 10 b) An AC controller is as shown in figure below has a resistive load R = 10Ω and the rms input voltage is 120V at 60Hz. The thyristor switch is on for n = 25 cycle and is off for m = 75 cycles. Determine (a) rms output voltage V 0 (b) input power factor pf (c) the average and rms current of thyristor a) How are choppers classified? Explain them briefly. 08 b) A step-down chopper is feeding an RL load with V s = 230V, R = 5Ω, L = 7.5mH, f = 1KHz, K = 0.5 and E = 0V. Calculate (a) The minimum instantaneous load current I 1 (b) The peak instantaneous load current I 2 (c) The maximum peak to peak load ripple current (d) The average value of load current I a (e) The rms load current I 0 (f) The effective input resistance R I seen by the source (g) the rms chopper current I R a) With the help of neat diagram and associated waveforms describe the operation of a BUCK regulator. 12 b) What is the principle of closed loop control of DC drives? 08 MVJCE 32 COURSE DIARY

33 Model Question Paper-II Duration: 3 Hrs Max. Marks: 100 Answer any five questions 1. a. Using two transistor analogy, derive the expression for the anode current of a Thyristor. 07 b. Explain the need to limit dv/dt and di/dt in a Thyristor. 06 c. A Thyristor has a forward characteristics which may be approximately over its normal working range to the strength line in a V-I characteristics curve (a) a continues ON state current of 23A. (b) a half-sine wave of mean value 18A. (c) a level current of 39.6 A for one half-cycle (d) a level current of 48.5A for one third cycle a. Explain the switching characteristics of IGBT. Mention its advantages over BJT. 10 b. Explain the significance of (i) current rating (ii) voltage rating of a thyristor a. Explain with relevant waveforms, derive expression for I DC, I RMS, V DC, V RMS, p.f. for single phase full converter for R-load. 10 b. A three-phase full converter is supplied from a three phase 230V, 60Hz supply. The load current is continuous and has negligible ripple. If the average load current I dc = 150A and the commutating inductance L c = 0.1mH determine the overlap angle when (a) α = 30 and (b) α = a. With the help of neat diagram and associated waveforms, explain the operation of three-phase half wave controlled rectifier supplying a resistive load. 10 b. A single phase semi-converter has a purely resistive load of R and the delay angle is α= π/2, determine (a) the rectification efficiency (b) the form factor FF (c) the ripple factor RF (d) the peak inverse voltage of thyristor a. With the help of a neat diagram, explain the operation of a resonant pulse chopper circuit.10 b. Design the values of commutating L m and C (in the impulse commutated chopper) circuit to provide a turn off time of 20µs. Assume V s = 600volts, I m = 350A, L s = 6µH. The peak current through T 1 is not to exceed 2I m a. What are the advantages and disadvantages of ON-OFF control? 06 b. A single-phase full-wave ac voltage controller has a resistive load of R= 10Ω and the input voltage is Vs = 120 V (rms), 60Hz. The delay angle of thyristors T 1 and T 2 are equal : α 1 = α 2 = α = π/2. Determine (a) the rms output voltage V 0 (b) the input power factor p.f. (c) the average current of thyristors I A, and (d) the rms current of thyristors I R, also derive the necessary formulae a. With the help of neat diagram and associated waveforms, describe the operation of step-up chopper supplying R-L load. 10 MVJCE 33 COURSE DIARY

34 b.the buck-boost regulator has an input voltage of V s = 12 V. The duty cycle K = 0.25 and the switching frequency is 25 KHz. The inductance L = 150µH and filter capacitance C = 220 F. The average load current I a = 1.25 A. Determine (a) the average output voltage V a (b) the peakto-peak ripple current of inductor I and (d) the peak current of the transistor, I p a. Develop the open loop transfer function model of a separately excited dc motor. Explain how could be the model be used to find the response due to changes in reference voltage and load torque. 10 b.the step-down dc chopper has a resistive load, R = 20Ω and input voltage, V s = 220 V. When the chopper remains on, its voltage drop is V ch = 1.5 V and chopping frequency is f = 10KHz if the duty cycle is 80%, determine (a) the average output voltage V a (b) the rms output voltage V 0 (c) the chopper efficiency (d) the effective input resistance R i and (e) the rms value of the fundamental component of harmonics in the output voltage. MVJCE 34 COURSE DIARY

35 10EE46 TRANSFORMERS AND INDUCTION MACHINES MVJCE 35 COURSE DIARY

36 SYLLABUS SUBJECT CODE: 106EE46 IA MARKS: 25 SUBJECT: TRANSFORMERS AND INDUCTION MACHINES EXAM HOURS: 3 EXAM MARKS: 100 HOURS / WEEK: 04 TOTAL HOURS: 52 PART A UNIT 1: Basic Concepts: Principle of operation of transformer, Constructional details of shell type and core type single-phase and three-phase transformers. EMF equation, operation of practical power transformer under no load and on load (with phasor diagrams).concept of ideal transformers, current inrush in transformers. 6 Hours UNIT 2: Single-phase Transformers: Equivalent circuit, losses, efficiency, condition for maximum efficiency, all day efficiency. Open circuit and Short circuit tests, calculation of parameters of equivalent circuit. Regulation, predetermination of efficiency and regulation. Polarity test, Sumpner s test. 6 Hours UNIT 3: Parallel operation - need, conditions to be satisfied for parallel operation. Load sharing in case of similar and dissimilar transformers. Auto-transformers, copper economy. Brief discussion on constant voltage transformer, constant current transformer. 6 Hours UNIT 4: Three-phase Transformers: Introduction, choice between single unit three-phase transformer and bank of single-phase transformers. Transformer connection for three phase operation star / star, delta / delta, star/delta,zigzag/star and vee/vee,choice of connection. Phase conversion - Scott connection for three-phase to two-phase conversion. Labeling of three-phase transformer terminals, phase shift between primary and secondary and vector groups. Conditions for parallel operation of three-phase transformers,load sharing. Equivalent circuit of three-phase transformer. 8 Hours PART B UNIT 5: Basic Concepts of three phase Induction Machines: Concept of rotating magnetic field. Principle of operation, construction, classification and types - single-phase, three-phase, squirrel-cage, slip-ring. Slip, torque, torque-slip characteristic covering motoring, generating and braking regions of operation. Maximum torque. 7 Hours UNIT 6: Three-phase Induction Motor: Phasor diagram of induction motor on no-load and on load. equivalent circuit Losses, efficiency, No-load and blocked rotor tests. Circle diagram and performance evaluation of the motor. Cogging and crawling. 6 Hours UNIT 7: High torque rotors-double cage and deep rotor bars.equivalent circuit and performance evaluation of double cage induction motor. Induction generator externally excited and self excited. Importance of induction generators in windmills. 6 Hours MVJCE 36 COURSE DIARY

37 UNIT 8: (a) Starting and speed Control of Three-phase Induction Motors: Need for starter. Direct on line (DOL), Star-Delta and autotransformer starting. Rotor resistance starting. Soft(electronic) starters. Speed control - voltage, frequency, and rotor resistance. 4 Hours (b) Single-phase Induction Motor: Double revolving field theory and principle of operation. Types of single-phase induction motors: split-phase, capacitor start, shaded pole motors. Applications. 3 Hours Text Books 1.Electric Machines, I. J. Nagrath and D. P. Kothari, T.M.H, 4 th Edition, Electric Machines, Mulukuntla S.Sarma, Mukesh K.Pathak, Cengage Learing,First edition,2009. References 1. Performance and Design of A.C. Machines, M. G. Say,C.B.S. Publishers, 3 rd Edition, Theory of Alternating Current Machines, Alexander Langsdorf, T.M.H, 2 nd edition, Electrical Machines and Transformers, Kosow, Pearson, 2 nd edition, Transformers, BHEL, TMH,2 nd Edition, Eight reprint MVJCE 37 COURSE DIARY

38 LESSON PLAN UNIT NO. TRANSFORMER & INDUCTION MACHINES Sub_Code : 10EE46 IA Marks: 25 Hrs/Week : 05 Exam Hrs: 03 Total Hrs : 60 Exam Marks: 100 UNIT NAME NO OF HOURS TOPICS TO BE TAKEN 1 Concept of coupled circuits. Dot convention. 1 Basic concepts 2 Single-phase Transformers 3 Transformer test 2 Writing network equilibrium equations in coupled circuits Principle of Transformer action for voltage Transformation, 3 Construction of shell, core type of 1 phase& 3 phase Transformers 4 power transformer, distribution transformer 5 Constant Voltage, Constant Current Transformers 6 Variable Frequency transformers 7 Autotransformers Concept of ideal transformer. Equation for E.M.F. 8 induced in the two windings. Voltage transformation ratio. Ideal transformer on noload and loaded condition with phasor diagram 9 Concept of M.M.F. balance in the magnetic circuit of an 10 ideal transformer. Current transformation ratio Concept of referring impedance connected on one side of 11 ideal transformer to the other side. Practical transformer how it deviates from the ideal 12 transformer. Development of exact equivalent circuit of a practical transformer visualization of a practical transformer as an ideal 13 transformer combined with imperfections of electric and magnetic circuits 14 Approximate equivalent circuit of a practical transformer Concept of ideal transformer, EMF Equation of 15 Transformer Phasor diagram of a practical transformer for both noload and loaded conditions Losses, power and all-day efficiency, regulation. Explanation of polarity test 18 Explanation of O.C & S.C test on transformer Explanation of how to pre-determine efficiency and 19 regulation using these tests 20 Problem on Equivalent Circuits Solving problems on losses in a transformer and hence to 21 determine efficiency & regulation Solving problems on O.C & S. C test and hence to find Efficiency & Regulation 22 Explanation of All Day Efficiency Solving problem on the same Explanation of Sumpner s Test 23 Comparison with O.C & S.C- Test Solving problems on the same Parallel operation need, conditions to be satisfied for 24 parallel operation. Load sharing. MVJCE 38 COURSE DIARY