College - Tele Syllabus - Sem 3

Applied Mathematics III

Complex Variables :  Functions of complex variables, continuity( only statement ), derivability of a function, analytical regular function, necessary condition for a function to be analytic, statement of sufficient conditions, Cauchy Riemann equations in polar co-ordinates. Harmonic functions, orthogonal trajectories, Analytical and Milne Thomson method to find f(z) from its real or imaginary part. Mapping- conformal mapping, linear and bilinear mapping with geometrical interpretations.

Fourier Series and Integrals. Orthogonal and orthonormal functions, expression of a function in a series of orthogonal functions, sine and cosine functions and their orthogonality properties. Fourier series, Drichlet conditions ( only statement ), periodic functions, even and odd functions, half range sine and cosine series, Parseval's relation. Complex form of Fourier series, introduction to Fourier integral, relation with Laplace transform.

Laplace Transforms. Function of bounded variable ( statement only ), Laplace transforms of 1, at, exp( at ), sin( at ), cos( at ), sinh( at ), cosh( at ), erf( t ), shifting properties, expressions with proofs for L { t f(t) }, L { f(t)/t }, Laplace of an integral and derivative. Unit step functions, Heavyside, Dirac Delta functions and their Laplace transform, Laplace transform of periodic functions. Evaluation of inverse Laplace transforms, partial fraction method, Heavyside development, Convolution theorem. Application to solve initial and boundary value problems involving ordinary differential equations with one variable.

Matrices. Types of matrices, adjoint of a matrix, inverse of a matrix, elementary transformations, rank of a matrix, linear dependent and independent rows and columns of a matrix over a real field, reduction to a normal form, partitioning of matrices System of homogenous and non homogenous equations, their consistency and their solutions.

Electronics I

Application of diodes as rectifiers. Filter analysis and specifications of the devices and components required for C, L, LC, CLC & RC filters. Single and double ended clipping circuits, clamping circuits.

Bipolar Junction Transistors. Introduction to biasing, modelling, Derivation and analysis of different types of transistor models, viz. h-parameter model, r-parameter model, hybrid pi model, high frequency model. Analysis of biasing circuits, fixed bias, collector to base bias and voltage divider bias. Calculation of stability factors. Thermal stabilisation and compensation, thermal runaway. Amplification, derivation of expressions for voltage gain, current gain, input impedance and output impedance of CC, CB & CE amplifiers.

Field Effect Transistors. Characteristics and coefficients, biasing circuits for FET amplifiers, AC equivalent circuit of FET. Derivation of expressions for voltage gain and output impedance of CS, CD & CG amplifiers.

BJT as a switch Analysis in transient and steady state.

Design of CE and CS single stage amplifiers. Designing using data sheets of appropriate components.

Voltage Regulators. Analysis of Zener, Series and shunt type of regulators.

Electrical Networks

Solution of Networks with dependant sources.

Linear graphs. Introductory definitions, The incidence matrix A, the loop matrix B, relationship between sub matrix of A and B. Cutsets and cutset matrix, Fundamental cutsets and fundamental tiesets, Planar graphs, A and B matrices, Loop, node, node pair equations, duality.

Network Equations. Time domain analysis, first and second order differential equations, initial conditions, evaluation and analysis of transient and steady state responses to step, ramp, impulse and sinusoidal input functions.

Laplace Transform. It's applications to analysis of network for different input functions described above.

Network Functions. Driving point and Transfer functions. Two port networks, open circuit and short circuit parameters, transmission parameters, hybrid parameters, chain parameters, interconnection of two port networks, cascade connection, series and parallel, permissibility of connection.

Representation of Network Functions. Pole, Zeros and natural frequencies, location of poles, even and odd parts of a function, magnitude and angle of a function, the delay function, all pass and minimum phase functions. Net change in angle, Azimuth polynomials, ladder networks, constant resistance network, maximally flat response, Chebyshev response, calculation of a network function from a given angle and a real part, Bode method.

Fundamentals of Network synthesis. Energy functions, passive reciprocal networks, the impedance function, condition on angle, positive real functions, necessary and sufficient conditions , the angle property of a positive real function, Bounded real function. Reactance functions, Realisation of reactance functions, ladder form of a network, Azimuth polynomials and reactance functions. Impedance and admittance of RC networks. Ladder network realisation, resistance inductance network.

Electrical Materials and Components.

Materials for resistors. Carbon, wire wound, film etc., conductors and switches, electrical conductivity of alloys, colour code for resistors, elastic and plastic deformation of solids, strain hardening, brittleness, fibre structure and directional properties, annealing, hot and cold working, soldering, brazing and welding process and materials, fluxes.

Semiconductors. Conduction process in semiconductor, electrical conductivity of p and n type semiconductors, diffusion process, pn junction and current flow in pn junction., breakdown in pn junction, hall effect and its measurements. Crystal growth ( especially epitaxial growth ) and I.C. fabrication. Materials for photoconductive, photoemissive and solar cell.

Dielectric properties of insulators. In static fields, polarization and dielectric constant. Dielectric constant of gases. The internal field in solids and liquids. Spontaneous polarization, ferroelectric materials. Types and values of condensers, temperature compensation, electrolytic capacitors. Insulators - dielectric properties, permitting polarization, dielectric loss, non linear dielectric material, piezo electricity, ferro electricity, breakdown of solid insulators.

Magnetic properties of materials. The magnetic dipole moment of current loop, diamagnetism, origin of permanent dipole moment in matter. Paramagnetism, ferromagnetism, hysteresis, spontaneous magnetisation and Curie- Weiss law. Ferromagnetic, ferrimagnetic and anti-ferromagnetic materials and the effect of hardening.

Components. Resistors, thermistors, varistors, selenium surge suppresors, variable resistors, potentiometers, variable capacitors, characteristics of capacitors, inductors, transformers for If and Hf applications, relays, fuses, characteristics, heat sink materials, switches, connectors.

Signals and Systems

Introduction: Basic signals in continuous and discrete time domain. Classification of signals: periodic / aperiodic, even/odd, deterministic/stochastic, energy/power. Signal representation in terms of orthogonal functions. Systems representation : forms of mathematical models of systems, systems classification, the normal form of systems equations, Discrete time system and difference equations, systems and signals properties.

Fourier analysis of continuous time signals Orthogonal functions, Fourier series representation in terms of sine , cosine, exponential. Complex Fourier series, Properties of Fourier series Convergence of Fourier series Gibbs phenomenon, Fourier transform & its properties, Fourier integrals, Discrete Fourier Transform and its properties. Fourier transform of singular functions Energy density spectrum

Convolution: Linear differential equations, Representation by impulses, systems impulse response & convolution integral. Evaluation & Interpretation of Convolution integral. System stability in time and frequency domain. Transient & steady state response of linear systems in terms of convolution sum and integral. Discrete convolution and deconvolution.

Laplace transform: Convergence, properties of Laplace transform, double sided transform, application of Laplace transform to solutions of differential equations, relationship between Fourier & Laplace transform.

Z-transform: Definition, convergence, properties & inversion of Z-properties, single & double sided transform. Analysis of discrete time systems using Z-transform Relationship between Laplace & Z-transform.

Time domain representation of LIZ systems in terms of differential equations and difference equations, classical methods of solutions to such equations.

State space Representation: Multi input multi output discrete and continuous systems. State model representation, Matrix representation of normal equations, time domain solutions of the state equations, state transition matrix.

Applications of transforms: Applications of transforms to discrete and continuous system analysis, concept of transfer function, notions of convergence and their interrelation with Laplace and Z transforms.

Electrical Technology and Instruments.

DC Motors. DC motors, E.M.F. equation, back emf of motors, torque equations, method of excitation, characteristics of DC shunt, series and compound motors. Speed - torque characteristics of DC motors. Starters, principles of speed control and braking.

Three phase Induction Motors. Rotating magnetic field, construction and principle of operation, slip, rotor frequency, development of equivalent circuit, torque equation, maximum torque, torque-speed characteristics, speed control, starting methods, motor ratings.

Single Phase Motors. Principles of operation and characteristics of single phase induction motor, capacitor, shaded pole, reluctance, hysteresis types, stepper motor.

Measuring Instruments. Principles of moving iron, moving coil, rectifier ammeters and voltmeters, principles of dynamometer- wattmeter and induction type energy meters, principles of p.f. meter and frequency meter, use of current and potential transformers.

Measurement of R,L,C. Measurement of low, medium and high resistance. Wheatstone and Kelvin bridge method. Ohm meters, Megohm bridge and megger. AC bridge circuits for measurement of inductance, capacitance and Q- factor. Schering Bridge.

Potentiometer. Principles of simple DC and AC potentiometers and their applications, DC vernier potentiometer.