Home » 2016 » August

# Monthly Archives: August 2016

## GATE syllabus for ECE 2017

EC Electronics and Communications

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 opamp
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.

## GATE VLSI Questions and answers

1) Why Silicon is preferred over Germanium in semiconductor devices?

– The major raw material for Si wafer fabrication is sand which is widely present in the nature.
– SiO2 which is a very good insulator can be easily processed. This layer of oxide is used for the gate oxide in MOSFET
-Temperature stability of silicon is good, it can withstand in temperature range typically 140C to 180C whereas Germanium is much temperature sensitive only up to 70C.

2) What is the difference between dry oxidation and wet oxidation and which is purest among these two?

Dry Oxidation

Si + O2 -> SiO2

This growth is relatively slow.But this process yields high quality oxide layers.

Wet Oxidation

Si +2H20 –> SiO2 + 2H2 ( Fast growth, less pure)

3) Effect of Body effect on Threshold Voltage if vsB > 0

Ans : We note that the voltage vSB (voltage source-to-body) is not
necessarily equal to zero (i.e., vSB > 0), which means that this voltage vSB will attract some electrons from the substrate (In Case of P Substrate), thus more voltage is needed to create the channel(SO THRESHOLD VOLTAGE INCREASES).

4) In MOSFET, the polarity of the inversion layer is same as that of (GATE 1989)

a) Charge on the gate electrode
b) Minority carriers in the drain
c) Majority carriers in the substrate
d) Majority carriers in the source

Ans : d

5) In an n-MOSFET, the susbstrate is

a) Heavily doped p type
b) lightly doped p type
c) heavily doped n type
d) lightly doped n type

Ans : a

( Why P+ is used ahead of P-, post your observations in comment section)

6) Vt of n-MOSFET is 0.5V. It is biased with $V_{GS}$= 3V, $V_{DS}=1V$, then the MOSFET is in

a) Cut-off
b) Saturation
c) Linear
d) Inverse Saturatiom

## What to expect from GATE ECE 2017 which is conducted by IIT Roorkee?

As GATE 2017 is hardly 4-5 months away, every aspiring student across the country will have one question in the mind. “What to expect from GATE ECE 2017 which is conducted by IIT Roorkee?”

Even though GATE examination papers will be formed by a committee consisting of faculty from all over the India. After years of analyzing, one can say that some IIT’s are known for some branches and one can expect “Really good questions”(WE mean TOUGH) in that particular GATE paper than the other branch paper. Keeping that in mind one can predict the difficulty of GATE paper off the top of one’s head.

This year, GATE examination will be conducted by IIT Roorkee and here are some important dates which are already published.

IIT Roorkee is very famous for Civil Engineering so one can expect some interesting questions in that dept. However, we from a family of Electronics and communication can breath a sigh of relief for sometime. IIT Roorkee previously conducted the GATE examination in the year 2009. And if we analyze the difficulty of EC paper in the year 2009, it was relatively easy. So, we may expect a moderate ECE paper this year.

Any GATE paper will be formed in such a way that it will test student’s understanding of basic concepts, logic, numerical ability, aptitude and some questions will be twisted to test one’s deep understanding of the subject.
Emphasis on any of above aspects will purely depend on the committee formed during that academic year.

Though one cannot predict 100% that the GATE exam will be easy, moderate or difficult, some old school tricks will help you to excel.

– Solving previous examination questions of last 15 years.
– Concentrating on Important topics and studying based on mark distribution which will be put up on website(http://www.iitr.ac.in)

All the best for your GATE preparation

Regards
gateece.org

## GATE Electromagnetic question and solution

In this post, we will see how to approach an electromagnetics question which had appeared in GATE 1995 for 2 marks.

Soln: First, let’s understand the question and draw a rough figure based on the question

As you see, the current direction is towards Z axis. Now the first question is to find out the direction of Magnetic field.

Can the Magnetic field exist in Z direction – No because Magnetic field is perpendicular to the direction of current.

Can the Magnetic field exist in Y direction? Let’s analyse that. Just take two current lines flowing from a plane Y=0, in this case, current is coming out of OUR computer screen, so according to right hand rule, the magnetic field will be in the anti-clockwise direction.

As you can see the magnetic field at the point due to the 2 current lines is only towards -x direction, thus magnetic field due to infinite current lines contributes only in -x direction and all the y components will be cancelled out.

Now In order to calculate the magnetic field due to the uniform current flowing in the Y=0 plane, we need to consider the small portion of the surface and draw appropriate ‘Amperian loop’ enclosing the current and apply Ampere’s law. In this case the amperian loop will be a rectangular box which is parallel to XY plane and extending an equal distance above and below the surface as shown in the above figure(1).

Applying Ampere’s law

$\oint_{C} \vec B. \vec dl$ = 2Bl=$\mu_o I_{enc}$=$\mu_o Kl$ where K= Current/metre

So in this case

B=$-\mu_o/2 K$
H= -K/2 $a^x$ where K=30 mA/m

So the correct Answer is H= -15 $a^x$ mA/m

## Electromagnetics question for GATE ECE 2017

There will be questions related to Electromagnetics in every GATE paper. Electromagnetics is one such subject where primary focus should be on understanding Maxwell’s equations(Concepts, forms and different types of problems). One should have thorough understanding of vector calculus and integration to come out on top. Try to get the below questions right. More questions will follow in future posts.

1) An electron traveling horizontally enters a region where a uniform electric field is
directed upward. What is the direction of the force exerted on the electron once it
entered the field?
(a) To the left
(b) To the right
(c) Upward
(d) Downward

Ans: d

2) Point charges 30 nC, -20 nC, and 10 nC are located at (-1,0,2), (0,0,0), and (1,5,-1)
respectively. The total flux leaving a cube of side 6 m centered at the origin.
(a) -20 nC
(b) 10 nC
(c) 20 nC
(d) 60 nC

Ans : b

3) Plane z = 10 m carries charge 20 nC/m2 . The electric field intensity at the origin
is
(a) -10 ˆaz V/m
(b) -18π aˆz V/m
(c) -72π aˆz V/m
(d) -360π aˆz V/m

Ans : d

4) Consider the following cases:
• A point charge Q is placed at the origin. Let D1 be the flux due to this charge
over a sphere of radius b centered at the origin.
• A uniformly charged sphere of radius a(a<b) centered at the origin with a
total charge of Q. Let D2 be the flux due to this over a sphere of radius b
centered at the origin is.
Which of the following is true
(a) D1 = D2
(b) D1 is not equal to D2
(c) Under special conditions, D1 = D2

Ans: a

5) Two identical coaxial circular coils carry the same current I but in opposite directions.
The magnitude of the magnetic field −→B at a point on the axis midway
between the coil is
(a) Zero
(b) The same as that produces by one coil
(c) Twice that produced by one coil
(d) Half that produced by one coil

Ans: a

6) According to Ampere’s Law, the path integral $\oint_{C} \vec B. \vec dl$around the closed loop C is
given by

(a) µ0(I1 + I2 − I3)
(b) µ0(−I1 − I2 + I3)
(c) µ0(I1 + I2 + I3)
(d) −µ0(I1 + I2 + I3)

For any explanations , use comment section.

## GATE Signals and systems questions

1) Which of the following signal is not periodic?
a) sin 10$\pi$t
b) sin 31t
c)sin 10$\pi$t + sin 31t
d) sin(10$\pi$t +31)

2) The value of the integral $\int_{0}^{\infty} e^{-\alpha*t^2} \delta(t+10)$ dt is
a) 0
b) $e^{-100 \alpha}$
c) $e^{10 \alpha}$
d) $e^{100 \alpha}$

3) A system is defined by its input and output relationship y(t)=5x(t+3)+2 where y(t) and x(t) are the output and input respectively. The system is
a) Linear and Casual
b)Linear and non-casual
c) non-linear and casual
d) non-linear and non-casual

4) If the input-output relation of a system is y(t)=$\int_{-\infty}^{2t} x(\tau) d\tau$ then the system is
a) Linear, time invariant and unstable
b) linear ,non-causal and unstable
c) linear, causal and time invariant
d) non-causal, time invariant and unstable

5) Evaluate te function $\int_{0}^{\infty} t^2 \delta(t-3)$ dt
a) $e^{-t^2}$
b) $t^3/3$
c) $t^2(t-3)$
d) 9