1301: ENGINEERING MATHEMATICS 1I

Module 1

Matrices and Vector spaces: Rank of matrix, Echelon and normal form, Solutions of linear systems of algebraic equations, Eigen values and Eigen vectors, Cayley- Hamilton theorem (no proof). Vector Spaces- Subspaces,-Linear Independence of vectors-Linearspan-Dimension and Basis. Linear transformations.

Module 2

Fourier series and Fourier integrals: Fourier series of Periodic functions-Euler formulae for Fourier coefficients- functions having period 2π , arbitrary period- even and odd functions-half range expansions, Fourier integral, Fourier cosine and sine transformations, linearity property, transform of derivatives, convolution theorem (no proof)

Module 3

Laplace transforms: Linearity property, transforms of elementary functions, Laplace transforms of derivatives and integrals, differentiation and integration of transforms,convolution theorm (no proof), use of Laplace transforms in the solution of initial value problems, unit step function, impulse function - transform of step functions, transforms of periodic functions.

Module 4

Vector calculus : Scalar and Vector point functions-Gradient and directional derivative of a scalar point functions.- Divergence and Curl of a vector point functions- their physical meanings.Evaluation of line integral, surface integral and volume integrals, Gauss’s divergence theorem,. Stoke’s theorem (No Proof of these theorem), conservative force fields,scalar potential.

Text books:

1. R.K. Jain, S.R.K Iyengar: Advanced Engineering Mathematics, Narosa publishers.1991
2. C.R. Wilie & L.C. Barrett: Advanced Engineering Mathematics, MGH Co.

References

1. Larry C Andrews, Ronald C Philips: Mathematical Techniques fo Engineers & Scientists, PHI
2. M.C. Potter, J.L. Goldberg: Advanced Engineering Mathematics, Oxford universitypress
3. B. S. Grewal: Higher Engineering Mathematics, Khanna publishers,1986

1302 PROBABILITY AND RANDOM PROCESS

Module 1

Random Variables - Discrete and continuous random variables - Probability density functions and distribution functions - Mathematical Expectations - Properties - Mean and Variance -Joint moments, Moment-generating and characteristic functions and their applications, conditional expectation; covariance and correlation; independent, uncorrelated and orthogonal random variables, covariance matrix and properties- Central limit theorem. Some special distributions: Uniform, Gaussian and Rayleigh distributions; Binomial, and Poisson distributions; Multivariate Gaussian distribution. Vector-space representation of random variables, linear independence, inner product, Schwarz Inequality

Module 2

Random processes - Classification of random processes and examples - Continuous random process - Discrete random process - Continuous random sequence - Discrete random sequence - Stationary process and evolutionary process - Strict sense stationary process - Wide sense stationary process - Auto correlation, auto covariance and cross correlation - Their relation, properties and problems - Poisson process - Mean, variance, autocorrelation of the Poisson process - Properties

Module 3

Markov process - Classification of Markov process - Markov chain - Transition probability matrix. Ergodic process - Time average of random process - Power spectral density and its properties - Spectral representation of real WSS process - Wiener-Khinchin Theorem - Calculation of spectral density given the autocorrelation function

Module 4

Linear time invariant systems - WSS process as input, stationarity of the output, auto-correlation and power-spectral density of the output; examples with white-noise as input to the analog communication coherent & non coherent receiver (AM, FM & PM)


1303 NETWORK THEORY

Module 1

Circuit concepts–Circuit elements and networks, classifications; Energy sources- Dependent, independent, ideal and practical sources; Standard signals and Waveforms – periodic and non periodic signals, alternating currents and voltages, Step function, Ramp function, Impulse function; complex impedance; Methods of Analysing Circuits – Node analysis, Mesh analysis; Source Transformations; Circuit Theorems- Superposition, Thevenin’s, Norton’s, Reciprocity, Maximum Power Transfer; Resonance – Series, Parallel, Q, Bandwidth.

Module 2

Transients - DC and sinusoidal response of RL, RC and RLC circuits, Initial and final conditions, Rise and decay of current, Time constant; Laplace Transforms – Laplace transform of important Network functions; Application of Laplace Transforms in circuit analysis – circuit elements in S domain, Transient analysis of RL, RC, and RLC networks with impulse, step, exponential, pulse and sinusoidal inputs, Transfer function and Impulse function in circuit analysis; S domain analysis - complex frequency, transform impedance, Significance of poles and zeros, Restriction of poles and zeros in driving point and transfer functions, Ruth-Hurwitz criteria for stability of Network functions.

Module 3

Characterization of two port networks using different parameters – Z, Y, Hybrid and Transmission parameters; Interconnections of two port Networks – Cascade, Series and Parallel, T and π representation of two port Networks;Passive filters – Filter fundamentals, Classification of Filters, Characteristic impedance, Transfer function, frequency response; Design of Constant K - Low Pass, High Pass, Band Pass & Band Reject Filters - T and ; Design of m derived Low Pass and High Pass filters - T and  ; Attenuators – T and π; Equalizers – Series and shunt.

Module 4

Realizability and Synthesis of passive networks – causality, stability, Hurwitz polynomial, Positive real functions, driving point immitance; Basic Philosophy of synthesis- removal of a pole at infinity, removal of a pole at origin, removal of conjugate poles, removal of a constant, Impedance and admittance functions, Foster’s method, Cauer method.


1304 DIGITAL ELECTRONICS

Module 1

Number system and codes : Binary , Octal, and Hexa-decimal number systems - Binary arithmetic, Binary coded Decimal, Excess - 3 code, Gray Code, Error detection and correction: parity, CRC, 7 bit Hamming code .Boolean algebra -minimization of Boolean function using Karnaugh Map (up to 6 variables) and Quine - McClusky methods. Formation of switching functions from word statements, realisation using basic gates and universal gates

Module 2

Combinational circuits: Half adder, Full adder, Subtractor, Binary Parallel adder, Carry look ahead adder, BCD adder, multiplexer, demultiplexer, decoder and encoder circuits. Implementation of simple combinational circuits using ROM and PLA.

Module 3

Sequential circuits: Flip-flops - RS /JK / T / D flip- flops, shift registers - counters -asynchronous and synchronous counters, Up-Down counter, Ring counter, Johnson counter - sequence generators - state table and diagrams. Arithmetic circuits: Serial Adder, Difference between parallel adder and serial adder, Binary multiplication, Binary division circuits

Module 4

Logic families: Standard logic levels - Current and voltage parameters - fan in and fan out - Propagation delay, noise consideration. Basic idea of DCTL, RTL and DTL families. TTL family NAND gate working principle, need for totem pole configuration, TTL inverter characteristics, Open collector gate and tri- state logic gate. CMOS: characteristics of basic CMOS inverter - interfacing of CMOS to TTL and interfacing of TTL to CMOS, Merits and demerits of TTL family and CMOS family. ECL family OR-NOR gate working principle.


1305 SOLID STATE ELECTRONICS

Module 1

Introduction to quantum mechanics, potential well problem, energy momentum relation for electrons in solids, effective mass and tunneling. Energy bands in solids, intrinsic and extrinsic semiconductors. Elemental and compound semiconductors.Fermi-diracdistribution.Equilibrium and steady state conditions, Equilibrium concentration of electrons and holes. Temperature dependence of carrier concentration.Carrier transport in semiconductors – drift, conductivity and mobility, variation of mobility with temperature and doping, High Field Effects, Hall effect.Excess carriers in semiconductors – Generation and recombination mechanisms of excess carriers, quasi Fermi levels, diffusion, Einstein relations. Continuity equations, Diffusion length - Gradient of quasi Fermi level.

Module 2

PN junctions - Contact potential, Electrical Field, Potential and Charge Density at the junction, Energy band diagram, Minority Carrier Distribution, Ideal diode equation, Electron and hole component of current in forward biased p-n junction, piecewise linear model of a diode effect of Temperature on I-V characteristics. Diode capacitances, switching transients. - Zener and avalanche break down, Metal Semiconductor contacts, Ohmic and Rectifying Contacts, Hetero Junctions – Energy band diagram, Applications.

Module 3

Field Effect Transistors: JFET - principle of operation, current equation, static I-V characteristics. MOS Capacitor – Ideal MOS Capacitor-MOS Electrostatics -accumulation, depletion & inversion- Energy Band Diagram, C-V characteristics, frequency effect- threshold voltage (derivation needed).MOSFET- Basic structure and principle of operation, I-V characteristics, Derivation of Drain Current and device parameters.

Module 4

Bipolar junction transistor - current components, Minority Carrier Distributions basic parameters, relations between alpha & beta - comparison Ebbers - Moll model, Switching, Base width modulation, Avalanche multiplication in collector-base junction, Punch Through, Base resistance, Static I-V characteristics of CB and CE configurations- frequency limitation of transistor - transit time effect


1306 ELECTRONIC CIRCUITS I

Module 1

Pulse characteristics - Pulse shaping using RC circuits, RC low pass- high pass-circuits, integrator and differentiator using RC, Diode circuits clipping & clamping circuits. Rectifiers - half wave, full wave, bridge - expression for ripple factor, efficiency, comparison, diode ratings. Filters - capacitor - inductor LC filters- use of bleeder resistor - voltage multipliers, DC power supply - simple voltage regulator using zener diode.

Module 2

BJT Amplifiers: Units of gain, CE amplifier- Biasing techniques - stabilization of operating point -Temperature compensation techniques- low frequency equivalent circuits - r-parameters, h-parameters Methods of coupling - D.C coupled amplifier - CE RC coupled amplifier - loading effect at the input and output - emitter follower as Buffer stage- Darlington emitter follower - Boot strapping - frequency response of RC coupled amplifier - frequency analysis of R C coupled amplifier - lower cut-off frequency - upper cut-off frequency - 3 db bandwidth.

Module 3

FET Amplifier: FET biasing- Low frequency equivalent circuit- RC coupled common source amplifier - expression for gain - frequency response - MOSFET V-I characteristics, load lines, small signal parameters, small signal equivalent circuits - Body effect - Biasing of MOSFETs amplifiers. Analysis of Single stage discrete MOSFET amplifiers – small signal voltage and current gain, input and output impedance of Basic Common Source amplifier, Common Source amplifier with and without source bypass capacitor, Source follower amplifier.

Module 4

High frequency equivalent circuits of BJTs, MOSFETs, Miller effect, short circuit current gain, s-domain analysis, amplifier transfer function. Analysis of high frequency response of Amplifiers. Pulse response of amplifiers Power amplifiers: Class A, B, AB and C circuits - efficiency and distortion. Biasing of class AB circuits. Transformer less power amplifiers.