Section 1: Engineering Mathematics

Linear  Algebra:  Vector  space,  basis,  linear  dependence  and  independence,  matrix algebra,  eigen  values  and  eigen  vectors,  rank,  solution  of  linear  equations  –  existence and uniqueness.

Calculus: Mean value theorems, theorems of integral calculus, evaluation of definite and improper integrals, partial derivatives, maxima and minima, multiple integrals, line, surface and volume integrals, Taylor series.

Differential  Equations:  First  order  equations  (linear  and  nonlinear),  higher  order  linear differential equations, Cauchy’s and Euler’s equations, methods of solution using variation of  parameters,     complementary  function  and  particular  integral,  partial   differential equations, variable separable method, initial and boundary value problems.

Vector Analysis: Vectors in plane and space, vector operations, gradient, divergence and curl, Gauss’s, Green’s and Stoke’s theorems.

Complex   Analysis:   Analytic   functions,   Cauchy’s   integral   theorem,   Cauchy’s   integral formula; Taylor’s and Laurent’s series, residue theorem.

Numerical Methods: Solution of    nonlinear equations, single and multi-step methods for differential equations, convergence criteria.

Probability and  Statistics:   Mean, median, mode  and  standard  deviation; combinatorial probability, probability distribution  functions –  binomial, Poisson, exponential and normal; Joint and conditional probability; Correlation and regression analysis.

Section 2:  Networks, Signals and Systems

Network  solution  methods:  nodal  and  mesh  analysis;  Network  theorems:  superposition, Thevenin and Norton’s, maximum power transfer; Wye‐Delta transformation; Steady state sinusoidal analysis using phasors; Time domain analysis of simple linear circuits; Solution of network  equations  using  Laplace  transform;  Frequency  domain  analysis  of  RLC  circuits; Linear 2‐port network parameters: driving point and transfer functions; State equations for networks.

Continuous-time  signals:  Fourier  series  and  Fourier  transform  representations,  sampling theorem  and  applications;  Discrete-time  signals:  discrete-time  Fourier  transform  (DTFT), DFT,  FFT,  Z-transform,  interpolation  of  discrete-time  signals;  LTI  systems:  definition  and properties, causality, stability, impulse response, convolution, poles and zeros, parallel and cascade  structure,  frequency  response,  group  delay,  phase  delay,  digital  filter  design techniques.

Section 3:  Electronic Devices

Energy  bands  in  intrinsic  and  extrinsic  silicon;  Carrier  transport:  diffusion  current,  drift current,  mobility  and  resistivity;  Generation  and  recombination  of  carriers;  Poisson  and continuity equations; P-N junction, Zener diode, BJT, MOS capacitor, MOSFET, LED, photo diode  and  solar  cell;  Integrated  circuit  fabrication  process:  oxidation,  diffusion,  ion implantation, photolithography and twin-tub CMOS process.

Section 4:  Analog Circuits

Small  signal  equivalent  circuits  of  diodes,  BJTs  and  MOSFETs;  Simple  diode  circuits: clipping,  clamping  and  rectifiers;  Single-stage  BJT  and  MOSFET  amplifiers:  biasing,  bias stability,  mid-frequency  small  signal  analysis  and  frequency  response;  BJT  and  MOSFET amplifiers:  multi-stage,  differential,  feedback,  power  and  operational;  Simple  op-amp circuits; Active filters; Sinusoidal oscillators: criterion for oscillation, single-transistor and op- amp configurations; Function generators, wave-shaping circuits and 555 timers; Voltage reference circuits; Power supplies: ripple removal and regulation.

Section 5:  Digital Circuits

Number systems; Combinatorial circuits: Boolean algebra, minimization of functions using Boolean    identities    and    Karnaugh    map,    logic    gates    and    their    static    CMOS implementations,  arithmetic  circuits,  code  converters,  multiplexers,  decoders  and  PLAs; Sequential circuits: latches and flip‐flops, counters, shift‐registers and finite state machines; Data converters: sample and hold circuits, ADCs  and   DACs; Semiconductor  memories: ROM, SRAM, DRAM; 8-bit microprocessor (8085): architecture, programming, memory and I/O interfacing.

Section 6:  Control Systems

Basic  control  system  components;  Feedback  principle;  Transfer  function;  Block  diagram representation;  Signal  flow  graph;  Transient  and  steady-state  analysis  of    LTI  systems; Frequency response; Routh-Hurwitz and Nyquist stability criteria; Bode and root-locus plots; Lag,  lead  and  lag-lead  compensation;  State  variable  model  and  solution  of  state equation of LTI systems.

Section 7:  Communications

Random processes: autocorrelation and power spectral density, properties of white noise, filtering  of  random  signals  through  LTI  systems;  Analog  communications:     amplitude modulation and demodulation, angle modulation and demodulation, spectra of AM and FM,  superheterodyne  receivers,  circuits  for  analog  communications;  Information  theory: entropy,  mutual  information  and  channel  capacity  theorem;  Digital  communications: PCM,  DPCM,  digital  modulation  schemes,  amplitude,  phase  and  frequency  shift  keying (ASK,  PSK,  FSK),  QAM,  MAP  and  ML  decoding,  matched  filter  receiver,  calculation  of bandwidth,   SNR   and   BER   for   digital   modulation;   Fundamentals   of   error   correction, Hamming codes; Timing and frequency synchronization, inter-symbol interference and its mitigation; Basics of TDMA, FDMA and CDMA.

Section 8:  Electromagnetics

Electrostatics; Maxwell’s equations: differential and integral forms and their interpretation, boundary  conditions,  wave  equation,  Poynting  vector;  Plane  waves  and  properties: reflection  and  refraction,  polarization,  phase  and   group  velocity,  propagation  through various   media,   skin   depth;   Transmission   lines:   equations,   characteristic   impedance, impedance     matching,     impedance     transformation,     S-parameters,     Smith     chart; Waveguides:   modes,   boundary   conditions,   cut-off   frequencies,   dispersion   relations; Antennas:  antenna  types,  radiation  pattern,  gain  and  directivity,  return  loss,  antenna arrays; Basics of radar; Light propagation in optical fibers.