Matrix algebra
Systems of linear equations
Eigen values and Eigen vectors
First order ( linear and non – linear ) equations
higher order linear equations with constant coefficients
Euler – Cauchy equations
Laplace transform and its application in solving linear ODEs
Initial and boundary value problems.
separation of variables
solutions of onedimensional diffusion equation
first and second order one – dimensional wave equation and two-dimensional Laplace equation.
Functions of single variable
Limit, continuity and differentiability
Mean value theorems
local maxima and minima
Taylor and Maclaurin series
Evaluation of definite and indefinite integrals
application of definite integral to obtain area and volume
Partial derivatives
Total derivative
Gradient
Divergence and Curl, Vector identities
Directional derivatives
Line, Surface and Volume integrals
Stokes
Gauss and Green's theorems.
Definitions of probability and sampling theorems
Conditional probability
Discrete Random variables
Poisson and Binomial distributions
Continuous random variables
normal and exponential distributions
Descriptive statistics – Mean, median, mode and standard deviation
Hypothesis testing.
Accuracy and precision
error analysis
Numerical solutions of linear and non – linear algebraic equations
Least square approximation
Newton's and Lagrange polynomials
numerical differentiation
Integration by trapezoidal and Simpson's rule
single and multi – step methods for first order differential equations.
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.
Fourier series and Fourier transform representations
sampling theorem and applications
Discrete – time signals
discrete – time Fourier transform ( DTFT ), DFT, FFT
Z – t ransform
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.
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.
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
differentialfeedback 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.
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.
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.
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.
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
propagation through various media
skin depth
Transmission lines equations
Characteristic impedance, impedence 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
A. Basic of sensors, Transducers.
B. Basic of data acquisition systems.
A. Discrete cosine transform
B. FIR, IIR, filter
C. Bilinear transformation.