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

GATE : Previous questions on Feedback Amplifier

GATE 1993
1) Negative feedback in Amplifiers

a) Improves the Signal to Noise ratio at I/p
b) Improves the Signal to Noise ratio at O/p
c) Does not improvee signal to noise ratio at I/o
d) Reduces distortion

Ans : d

GATE 1995
2) To obtain very high input impedance and output impedances in a feedback Amplifier , which is the suitable configuration

a) Voltage – Series
b) Current – Series
c) Voltage – Shunt
d) Current – Shunt

Ans : b

Note: Explanation is given after 3rd question.

GATE 1998
3) In a shunt-shunt negative feedback Amplifier, as compared to the basic Amplifer.

a) Both input and output impedance increases
b) Input impedance decreases, but output impedance increases
c) Input impedance increases, but output impedance decreases
d) both input and output impedance increases

Hint : Feedback topology naming convention goes this way

Shunt(I/P) – Shunt(O/P). Remember Shunt-Shunt is also called as Voltage – Shunt. You can read that HERE
Impedance at input or output side depends on the word Series/Shunt. If Series then impedance increases
and if Shunt, then impedance decrease. In this question, the feedback topology is shunt-shunt, hence the correct answer is option d.

Ans : d

GATE 1991

4) Two non-inverting amplifiers, one having a unity gain and other having a gain of twenty, are made using identical operational amplifiers. As compared to the unity gain amplifier, the amplifier with gain twenty has

a) less negative feedback
b) More input impedance
c) Less Bandwidth
d) None of the above

Ans : c

Try to dissolve the above question.

GATE : Transmission lines questions

1) Two very long loss-less cables of characteristic impedances of 50 $\Omega$ and 100 $\Omega$ respectively are to be joined for reflection less transmission. If the quarter wave transformer is used for matching, what should be the value of its impedance(in ohms)?

a) 70.7
b) 35.7
c) 50
d) 2

2) A transmission line with a characteristic impedance of 100 $\Omega$ is used to match a 50 $\Omega$ section to a 200 $\Omega$ section. If the matching is to be done both at 429MHz and 1GHz, the length of the transmission line can be approximately

a) 82.5cm
b) 1.05m
c) 1.58m
d) 1.75m

3) Impedance of a transmission line repeats itself every

a) $\lambda$/4
b) $\lambda$/2
c) $\lambda$
d) 2$\lambda$

4) If $Z_{open}$ is the impedance of a open circuited transmission line and $Z_{short}$ is the impedance of a short circuited transmission line whose characteristic impedance is $Z_o$. Then which of the following relationship is true?

a) $Z_o$ =$\frac{Z_{open}}{Z_{short}}$
b) $Z_o$ =$Z_{open}$ * $Z_{short}$
c) $Z_o$ =$\sqrt{\frac{Z_{open}}{Z_{short}}}$
d) $Z_o$ =$\sqrt {Z_{open}*Z_{short}}$

5) A transmission line of characteristic impedance 50 $\Omega$ is terminated by a 50 $\Omega$ load. When excited by a sinusoidal voltage source at 10 GHz, the phase difference between two points spaced 2 mm
apart on the line is found to be π/4 radians. The phase velocity of the wave along the line is

a) 0.8* $10^8$ m/s
b) 1.2*$10^8$ m/s
c) 1.6*$10^8$ m/s
d) 3*$10^8$ m/s

A transmission line of characteristic impedance 50 $\Omega$ is terminated in a load impedance . The
VSWR of the line is measured as 5 and the first of the voltage maxima in the line is observed at a
distance of $\lambda$/4 from the load. The value of $Z_L$ is
(A) 10 $\Omega$
(B) 250 $\Omega$
(C) (19.23 + j46.15) $\Omega$
(D) (19.23 – j46.15) $\Omega$

….

1-a, 2-c , 3-b, 4-d

Waveguide Questions for GATE EC

1) Which is the dominant mode in TM?
a) $TM_{10}$
b) $TM_{21}$
c) $TM_{01}$
d) $TM_{11}$

2) Dominant mode in Waveguides usually refers to ?

a) $TE_{10}$
b) $TM_{10}$
c) $TM_{01}$
d) $TM_{11}$

3) The cut-off wavelength of rectangular waveguide was measured to be 8 cm and 4.8 cm when excited in $TE_{10}$ and $TE_{11}$ modes respectively. Determine the dimensions of a waveguide

a= ______
b= ______

4) A rectangular waveguide has dimensions a=2.5 cm and b=1 cm. A microwave signal at a frequency if 8.6 GHz is to be propagated through this waveguide.Which of the following mode can exist in rectangular waveguide?

a) $TE_{10}$
b) $TM_{10}$
c) $TM_{01}$
d) $TM_{11}$

5) The modes in a rectangular waveguide are denoted by $TE_{mn}$/$TM_{mn}$ where m and n are the Eigen
numbers along the larger and smaller dimensions of the waveguide respectively. Which one of
the following statements is TRUE?

a) The mode $TM_{10}$ of the waveguide does not exist
b) The mode $TE_{10}$ of the waveguide does not exist
c) The $TE_{10}$ and $TM_{10}$ the modes both exist and have the same cut – off frequencies
d) The $TM_{10}$ and $TM_{01}$ the modes both exist and have the same cut – off frequencies

6) If $\lambda_c$ is the cut off wavelength of a rectangular waveguide and $\lambda_o$ is a free space wavelength. Then the condition for wave propagation is

a) $\lambda_c$ > $\lambda_o$
b) $\lambda_c$ < $\lambda_o$
c) $\lambda_c$ = $\lambda_o$
d) $\lambda_c$ = 0

7)

TE(02) means the wave exists only in the Y direction. So look out for Electric field lines which are originating or ending at Y axis. In this case, options A and C are eliminated. Now we are left with option b and d.

Here as you can see, TE(02) means n=2 (Mode is 2) . So the E field equation will be of the following form

$E_y$= K $sin(\frac{2\pi y}{b})$

Y axis range is from 0 to b.

At

y=0 and y=b, value of sin is 0.

At y=b/4,  value of sin is 1

At y=3b/4, value of sin is -1

So, the correct answer is option “d” , where E field lines are pointing towards positive x axis below b/2 and towards negative x axis above b/2

…………………………………………………………………………………………………….