College - Tele Syllabus - Sem 4

Applied Mathematics IV:

Complex Variables. Regions and paths in the Z plane. Path/Line integral of a function. Inequality conditions for a path integral to be independent of the path joining two points. Contour Integral, Cauchy's theorem for analytical functions with continuous derivatives. Cauchy Goursat theorem( statement only ) and its use for multiply connected regions. Cauchy's integral formula and deductions. Morera's theorem and maximum modulus theorem. Taylor's and Laurent's developments, Singularities, poles, residue at isolated singularity and its evaluation. Residue theorem - Application to evaluate real integrals.

Matrices. Brief revision of vectors over real field, inner product, normal, linear independence, orthogonality. Characteristic values and vectors, and their properties for Hermitian and real Symmetric matrices. Characteristic polynomial. Cayley Hamilton theorem, functions of a square matrix, minimal polynomial, diagonable matrix. Quadratic forms, orthogonal, congruent and Lagrange's reduction of quadratic forms, rank, index, signature of a quadratic form, value class of a quadratic form. Statement of bilinear form.

Vector Calculus. Scalar and Vector point functions, directional derivative, level surfaces, gradient, surface and volume integrals, definition of curl, divergence. Use of operator. Conservative, irrotational, solenoidal fields. Green's theorem for plane regions and properties of line integral in a plane, Statements of Stoke's theorem, Gauss Divergence theorem, related identities, deductions, statement of Laplace's differential equation in cartesian, spherical, polar and cylindrical co-ordinates.

Electronics II

Low and High frequency analysis of BJT and FET amplifier circuits.

Analysis of RC coupled amplifiers Cascode Amplifiers, Darlington pair and DC amplifiers. Design of two stage RC coupled amplifier.

Feedback Amplifiers.( Negative Feedback ) Introduction to negative and positive feedback, current, voltage, series and shunt feedback. Its effect on input impedance, output impedance, voltage gain, current gain and bandwidth.

Oscillators. Positive feedback, oscillators using feedback principle. Derivation for frequency of oscillation and conditions for maintenance of oscillations of ( i ) RC phase shift ( ii ) Wien Bridge ( iii ) Tuned collector / drain ( iv ) Tuned gate ( v ) Hartley / Colpitts ( vi ) Crystal Oscillators.

Analysis of Differential Amplifier. Discrete components, operational amplifiers ( ideal ), Basic Op-Amp circuits.

Relaxation Oscillator and Linear Sweep Circuits.

Analysis of large signal amplifiers. Class A, B, AB and C. Design of audio frequency power amplifiers of class A and class B type.

Special Devices. Photo sensitive devices, display devices and Schottky diode.

Principles of Communication Engineering

Signals and their representations. Fourier series, Fourier transform, continuous spectra, frequency selective networks and transformers.

Basic Information Theory. Information , entropy of discrete systems, rate of transmission, redundancy, efficiency and channel capacity.

Amplitude Modulation. Frequency spectrum, power relations, basic requirements and description of various modulators, comparison. DSB, DSBSC, SSB, VSB, spectrum modulators and detectors.

Frequency Modulation. Frequency spectrum of FM, phase modulation, effect of noise, generation of FM and demodulators.

Pulse Modulation. Sampling theorem, low pass and band pass signals, elements of PAM, PWM, PPM, PCM and Delta Modulation. FDM,TDM.

A.M. and FM radio transmitters and receivers. Characteristics, block diagrams.

Logic Circuits

Number systems and codes. Binary, Octal and Hexadecimal number systems. Conversion from any base to another base number system. Binary, BCD, Excess-3, Alphanumeric, EBCDIC, Hollerith, ASCII codes, code conversion, error detecting and correcting codes, parity and Hamming codes.

Binary Arithmetic. Basic rules for addition and multiplication. Sign magnitude notation, One's complement notation. Two's complement notation. Addition and multiplication using binary, octal and hexadecimal number systems.

Boolean Algebra and Logic Gates. Boolean algebra theorems, reduction of logic expressions using boolean algebra, truth tables, minterms, maxterms, SOP and POS forms. Standard SOP and POS forms. Basic and universal logic gates, control aspect of gates, enabling and disabling of gates. K map representation of logical functions, simplification of logic functions using K-maps upto 6 variables. Quine McCluskey method and Veitch diagrams used for logic function reduction.

Combinational Logic Circuits. Concepts of combinational and sequential logic circuits. Realisation of following circuits using gates.: ( a ) Systems implementing combinational logic. ( b ) Arithmetic circuits, half and full adders, subtractors, multipliers, code converters, parity generators, parity checkers, comparators. ( c ) Multiplexers, demultiplexers, encoder, decoder. ( d ) Concept of mode control ( e ) Application of MSI devices for multiplexer, demultiplexer / decoder, parity generator / checker, concept of capacity expansion using gates. Use of MSI devices for adders, Sequential adder, BCD adder / subtractor, carry look ahead adder, multiplier, fast multipliers, Arithmetic Logic Unit ( ALU )

Sequential Circuits. ( a ) Concept of Synchronous and Asynchronous operation. ( b ) Flip Flops : Basic cell, SR , clocked SR, D, T , J-K, J-K with preset and clear, Master Slave J-K flip flops. Concept of level triggering and edge triggering , flip flop excitation tables, triggering and timing of flip flops. ( c ) Registers : Shift registers, bi-directional, serial to parallel, parallel to serial conversion. ( d ) Analysis of clocked sequential circuits. ( e ) Asynchronous counters : up-down counters, modulo N counter, glitch problem. ( f ) Synchronous counters : Use of K- maps for synchronous counters, ring counters, twisted ring counters, counters using shift registers, sequence generators using flip flops.

Electromagnetic Fields and Waves

Static electric fields in vacuum: Coulombs law, electrostatic potential gradient, fields due to point, line surface & volume charges, electric dipoles & its field.

Dielectric media: Polarisation, surface & volume charge densities due to polarisation, Displacement vector, boundary conditions

Gauss law & its applications Laplace & Poisson's equations

Electrostatic energy & force: Energy of a charge distribution, energy density, pressure & forces.

Method of images: Point charge & a conducting plane.

Steady electric current: Current density, equation of continuity.

Static magnetic fields in vacuum: Lorentz force equation, Biot-Savarts law & its applications, Amperes circuital law & its applications Divergence and curl of B, magnetic scalar & vector potentials.

Electromagnetic induction: Faradays laws in integral & point form, simple problems. Summary of the results in the form of Maxwell's equations, modification of equations for time varying fields.

Uniform plane waves in free space: Derivation of wave equation & its solution in its simplest form, concept of space & time variations, E,H, & the direction of wave propagation, Intrinsic impedance, sinusoidally time varying uniform plane waves in free space, phase constant, wavelength, phase velocity, classification of waves for communication.

Numerical Methods and C Programming

Numerical Methods.

Errors in Numerical Computation. Their types, analysis and estimation.

Solutions to Transcendental and Polynomial equations. Bisection method, Secant method, Newton Raphson method for polynomial equations.

Solutions to System of Linear Algebraic Equations. Cramer's rule, Gauss elimination method, Gauss Jordan method, Triangularization methods- Gauss Siedel method of iteration.

Interpolation Linear interpolation and high order interpolation using Lagrange and Newton Interpolation methods, finite difference operators and interpolation polynomials using finite differences.

Numerical Differentiation. Methods based on interpolation and finite differences.

Numerical Integration. Trapezoidal rule, mid-point method, Simpson's 1/3rd and 3/8th rule.

Solutions to ordinary differential equations. Taylor series method, Euler's method, Euler's predictor and corrector method. Runge Kutta method for 2nd and 4th order.

C Programming:

Features of C, ANSI C, structure of a C program.

Character set, variable names, data types, constants and declarations, scope and lifetime of variables.

Arithmetic, logical, relational, increment, bitwise, assignment operators and expressions, conditional expressions, precedence of order of evaluation and type conversion.

Basic input and output, formatted input and output.

Control structures : Concept of a block statement. IF, IF-Else, Switch, Looping structures - FOR, DO, WHILE, Break and Continue statements, GOTO statement.

Functions : external variables, scope rules, nesting of functions, function of arrays.

Arrays : One dimensional, two dimensional and multi dimensional arrays, their initialisation and manipulation. String handling features.

Pointers : addresses, their initialisation, pointer arithmetic, pointers and functions, pointers and arrays, pointers to pointers, pointers to functions.

Pre processor : macro substitution, header file inclusion, study of standard libraries like stdio.h, ctype.h, string.h, math.h, stdlib.h, stdarg.h, dos.h etc.