GATE EC2003 question

Ans :
Number of Mesh = B - N + 1 where B = No of Branches
N = number of Nodes
Node equation = N - 1
where N = number of Nodes

here B = 7 , N = 4

so minium number of equation need to analyze the circuit is = N - 1 = 3

Qu(2):

The Laplace transform of of i(t) is given by
I(s) = 2 / s(1+s)
As t --> infinity, The value of i( t) tends to


Ans:
Inverse of I(s) ,
I(s) = 2/s -2/(1+s)
i(t) = 2 -2(e^-t) because L(1) = 1/s and L(e^-t .1) = 1/(S+1)
As t --> infinity ,
==> i(t) = 2 -2/(e^infinity)
==> i(t) = 2 - 2/infinity
== > i(t) = 2 because 2/infinity is zero

This is the answer I got. I am not sure about 2/infinity . ,,...

i don't know these answers are correct or not .. I didn't get key for GATE these question.

DIGITAL SIGNAL PROCESSING

I become a fan of Prof. S.C. Dutta Roy .....if you hear these videos then you will reach a new world. See some beautiful lectures ..

Brief Technical Biography of S C Dutta Roy

S C Dutta Roy , a Ph D from the Calcutta University, is currently an INSA Senior Scientist at the Electrical Engineering Department, IIT Delhi, where he served as a Professor for more than three decades. He has also held the positions of Head of the Department and Dean of Undergraduate Studies at IIT Delhi, and Visiting faculty positions at the University of Minnesota, USA ; University of Leeds, UK ; and the Iowa State University, USA. His research interests are in signal processing – analog as well as digital, and he has published extensively in IEEE, IEE and other professional journals of repute.

Professor Dutta Roy is a Fellow of the IEEE, the Acoustical Society of India, the Systems Society of India, and of all the Science and Engineering Academies of India, and is a Distinguished Fellow of the Institution of Electronics and Telecommunication Engineers (IETE), India. He has served on the Editorial Boards of a few IEEE and other prestigious international journals and all the national journals in his field. He received several prestigious national awards, including the Shanti Swarup Bhatnagar Prize, the Vikram Sarabhai Award and the Pandit Jawaharlal Nehru Award.

why derivatives ?

To find an approximation of one can do as follows.

1. Consider the function Hence, the problem is reduced to finding the value of f(25).
2. We have

   

3. According to linear approximation

   

4. The result, 2.926, lies fairly close to the actual value 2.924…

Read some interesting and basic mathematics.. http://en.wikipedia.org/wiki/Linear_approximation

LOST TOUCH WITH MATHS

Onam days I have tried some Laplace Transform ( which is commonly used in Network realization and ELECTRICAL circuits ) from mathematics text book. Then I realized the fact that even the basic integration methods like integration by parts and other haven't there in my mind. But the basic for mule in Laplace finished in onam days itself. Parallel y hearing online video classes ..... but it is like a drop of water in the sea....... I dont know where I can reach.

I am wasting precious time

Mind become restless if we can't utilize our time effectively. Nowadays I found that that was the major reason for my restlessness. Somewhere I need to concentrate my mind and brain. I am feeling that I am not utilizing the time given to me...

I don't know how to solve this problem..... But I am not ready to fear.


( this is today's state of mind )

GATE EXAM SYLLABUS

EC - Electronics and Communication Engineering

ENGINEERING MATHEMATICS

Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors.

Calculus:Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series. Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Greens theorems.

Differential equations:First order equation (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchys and Eulers equations, Initial and boundary value problems, Partial Differential Equations and variable separable method.

Complex variables:Analytic functions, Cauchys integral theorem and integral formula, Taylors and Laurent series, Residue theorem, solution integrals.

Probability and Statistics:Sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Discrete and continuous distributions, Poisson, Normal and Binomial distribution, Correlation and regression analysis.

Numerical Methods:Solutions of non-linear algebraic equations, single and multi-step methods for differential equations.

Transform Theory:Fourier transform, Laplace transform, Z-transform.

ELECTRONICS AND COMMUNICATION ENGINEERING

Networks: Network graphs: matrices associated with graphs; incidence, fundamental cut set and fundamental circuit matrices. Solution methods: nodal and mesh analysis. Network theorems: superposition, Thevenin and Nortons maximum power transfer, Wye-Delta transformation. Steady state sinusoidal analysis using phasors. Linear constant coefficient differential equations; time domain analysis of simple RLC circuits, Solution of network equations using Laplace transform: frequency domain analysis of RLC circuits. 2-port network parameters: driving point and transfer functions. State equations for networks.

Electronic Devices: Energy bands in silicon, intrinsic and extrinsic silicon. Carrier transport in silicon: diffusion current, drift current, mobility, and resistivity. Generation and recombination of carriers. p-n junction diode, Zener diode, tunnel diode, BJT, JFET, MOS capacitor, MOSFET, LED, p-I-n and avalanche photo diode, Basics of LASERs. Device technology: integrated circuits fabrication process, oxidation, diffusion, ion implantation, photolithography, n-tub, p-tub and twin-tub CMOS process.

Analog Circuits: Small Signal Equivalent circuits of diodes, BJTs, MOSFETs and analog CMOS. Simple diode circuits, clipping, clamping, rectifier. Biasing and bias stability of transistor and FET amplifiers. Amplifiers: single-and multi-stage, differential and operational, feedback, and power. Frequency response of amplifiers. Simple op-amp circuits. Filters. Sinusoidal oscillators; criterion for oscillation; single-transistor and op-amp configurations. Function generators and wave-shaping circuits, 555 Timers. Power supplies.

Digital circuits: Boolean algebra, minimization of Boolean functions; logic gates; digital IC families (DTL, TTL, ECL, MOS, CMOS). Combinatorial circuits: arithmetic circuits, code converters, multiplexers, decoders, PROMs and PLAs. Sequential circuits: latches and flip-flops, counters and shift-registers. Sample and hold circuits, ADCs, DACs. Semiconductor memories. Microprocessor(8085): architecture, programming, memory and I/O interfacing.

Signals and Systems: Definitions and properties of Laplace transform, continuous-time and discrete-time Fourier series, continuous-time and discrete-time Fourier Transform, DFT and FFT, z-transform. Sampling theorem. Linear Time-Invariant (LTI) Systems: definitions and properties; causality, stability, impulse response, convolution, poles and zeros, parallel and cascade structure, frequency response, group delay, phase delay. Signal transmission through LTI systems.

Control Systems: Basic control system components; block diagrammatic description, reduction of block diagrams. Open loop and closed loop (feedback) systems and stability analysis of these systems. Signal flow graphs and their use in determining transfer functions of systems; transient and steady state analysis of LTI control systems and frequency response. Tools and techniques for LTI control system analysis: root loci, Routh-Hurwitz criterion, Bode and Nyquist plots. Control system compensators: elements of lead and lag compensation, elements of Proportional-Integral-Derivative (PID) control. State variable representation and solution of state equation of LTI control systems.

Communications: Random signals and noise: probability, random variables, probability density function, autocorrelation, power spectral density. Analog communication systems: amplitude and angle modulation and demodulation systems, spectral analysis of these operations, superheterodyne receivers; elements of hardware, realizations of analog communication systems; signal-to-noise ratio (SNR) calculations for amplitude modulation (AM) and frequency modulation (FM) for low noise conditions. Fundamentals of information theory and channel capacity theorem. Digital communication systems: pulse code modulation (PCM), differential pulse code modulation (DPCM), digital modulation schemes: amplitude, phase and frequency shift keying schemes (ASK, PSK, FSK), matched filter receivers, bandwidth consideration and probability of error calculations for these schemes. Basics of TDMA, FDMA and CDMA and GSM.

Electromagnetics: Elements of vector calculus: divergence and curl; Gauss and Stokes theorems, Maxwells equations: differential and integral forms. Wave equation, Poynting vector. Plane waves: propagation through various media; reflection and refraction; phase and group velocity; skin depth. Transmission lines: characteristic impedance; impedance transformation; Smith chart; impedance matching; S parameters, pulse excitation. Waveguides: modes in rectangular waveguides; boundary conditions; cut-off frequencies; dispersion relations. Basics of propagation in dielectric waveguide and optical fibers. Basics of Antennas: Dipole antennas; radiation pattern; antenna gain.

DREAM FIRST ... WORK FOR IT, YOU WILL GET

DREAM FIRST .. WORK FOR IT , YOU WILL GET

I believe these words.


Some of college friends motivating me for a Mtech. Really my mind is restless now.

WARNING

how fast or immediate i am starting study and How fastly and strongly i studies subjects will determine my score in GATE ......



I am feeling that Mtech in IIT( dream) is reachable ambition. But I haven't informed this to father. Most probably he will reject....(that is not a problem )
I informed to my brother....( i got half +ve approval from him).I need to work hard that was his advice.
Here(in chennai) the atmosphere is not favor to study .It is a challenge as well as thrill.
Getting a Btech admission in IIT is much harder than a MTech. Making a decision is very important because GATE is an all India exam. Even if it is simple compared to btech, students from all over india is participating in it.That much competition is there.

( this blog is exclusively to me)