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ECE

1

ANALYSIS OF GATE 2019

Electronics and Communication Engineering

Engineering Mathematics

15%

Network Theory 8%

Signals and Systems 8%

Control Systems 8%

Analog Circuits 9% Digital Circuits

9%

Communications 5%

Electronic Device Circuits

15%

Electromagnetic Theory

8%

General Aptitude 15%

Memory Based

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ECE

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ECE ANALYSIS-2019_Feb-9_Morning

SUBJECT No. of Ques. Topics Asked in Paper(Memory Based) Level of

Ques. Total Marks

Engineering

Mathematics

1 Marks: 7

2 Marks: 4

Probability, Eigen values, Integral Calculus, Linear algebra, Complex variables,

Differential Equations Moderate 15

Network Theory 1 Marks: 2

2 Marks: 3 Two port network, Steady state analysis,

Time constant, transient analysis Moderate 8

Signals and

Systems

1 Marks: 2

2 Marks: 3 FFT ,Z-Transform, Digital filters, Time

period analysis Difficult 8

Control Systems 1 Marks: 2

2 Marks: 3 Bode Plot, Stability analysis, Signal flow

graph, Transfer function Moderate 8

Analog Circuits 1 Marks: 1

2 Marks: 4 Clipper, Zener diode, MOSFET Moderate 9

Digital Circuits 1 Marks: 5

2 Marks: 2

Combinational Circuits, Noise margin, CMOS logic, logic gates, sequential circuits,

State machine Moderate 9

Communications 1 Marks:1

2 Marks: 2 Hamming codes, Amplitude and frequency

modulation Moderate 5

Electronic Device

Circuits

1 Marks: 3

2 Marks: 6 CMOS inverter, BJT, Responsivity of photo

diode, Fermi level , Band diagram Difficult 15

Electromagnetic

Theory

1 Marks: 4

2 Marks: 2 Antenna, Maxwell Equations, Gauss law,

Wave light Moderate 8

General Aptitude 1 Marks: 5

2 Marks: 5 Data interpretation, Grammer, Seating

arrangement, Time and work Moderate 15

Total 65 100

Faculty Feedback Overall paper is moderate to difficulty level. Compared to last year, the 2019

ECE paper is easy



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GATE 2019 Examination* (Memory Based)

Electronics and Communication Engineering

Test Date: 9-FEB-2019

Test Time: 9.30 AM to 1:30 PM

Subject Name: Electronics and Communication Engineering

General Aptitude

Q.1 - Q.5 Carry One Mark each.

1. It would take one machine 4 hours to complete a production and another machine 2 hours

to complete the same order. If both machine work simultaneously at their respective

constant rates, the time taken to complete the same order is ______ hours. ( )

( ) 3

4

( ) 2

3

( ) 7

3

[Ans. A]

2. A When he didn’t come home, she ________ him lying dead on road side somewhere

(A) pictured

(B) notice

(C) concluded

(D) looked

[Ans. A]

3. The strategies that the company ________ to sell its products ________ house–to–house

marketing.

(A) uses, including

(B) uses, include

(C) used, includes

(D) use, includes

[Ans. B]

4. The boat arrived __________ drawn.

(A) under

(B) at



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(C) in

(D) on

[Ans. B]

5. Five different books (P, Q, R, S, T) are be arranged on a shelf. The books R and S are to be

arranged first and second respectively from right side of the shelf. The number of different

orders in which P, Q and T may be arranged is ________

(A) 6

(B) 2

(C) 12

(D) 120

[Ans. A]

Q.6 - Q.10 Carry Two Mark each.

6. Indian history was written by British historians – extremely well documented and

researched, but not always impartial. History had to serve its purpose. Everything was

made subsequent to the glory of union jack. Latter day, Indian scholars presented a

contrary picture.

From above we can infer that -

Indian history written by British Historians ___________.

(A) was well documented & researched but was sometimes biased.

(B) was well documented and not researched but was always biased.

(C) was not well documented & researched but was sometimes biased.

(D) was not well documented and researched but was sometimes biased.

[Ans. A]

7. Two design consultants P and Q, started working from 8 AM for a client. The client

budgeted a total of USD 3000 for the consultants. P stopped working when hour hand

moved by 210 degrees on the clock. Q stopped working when the hour hand moved by 240

degrees on the clock. P took two tea breaks of 15 minutes each during her shift, but took

no lunch break. Q took only one lunch break of 20 minutes, but no tea break. The market

rate for consultants USD 200 per hour and breaks are not paid. After paying the

consultants, the clients shall have USD __________remaining in the budget

(A) 433.33

(B) 000.00



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(C) 300.00

(D) 166.67

[Ans. D]

8. The bar graph in panel (a) shows the proportion of male and female illiterates in 2001 and

2011. The proportion of male and female in 2001 and 2011 are given in panel (b) and (c)

respectively. The total population did not change during their period.

The percentage increase in the total number of literates from 2001 and 2011 is

(A) 33.43

(B) 34.43

(C) 35.43

(D) 30.43

[Ans.D]

9. Four people are standing in a line facing you. They are Rahul, Mathew, Seema and Lohit.

One is engineer, one is a doctor, one a teacher and another a dancer.

You are told that:-

1. Mathew is not standing next to Seema.

2. There are two people standing between Lohit and engineer.

3. Rahul is not a doctor.

4. The teacher and the dancer are standing next to each other.

5. Seema is turning right to speak to the doctor standing next to her.

Who among them is an Engineer?

(A) Lohit

(B) Seema

(C) Rahul

(D) Mathew

[Ans. D]

60

40 50 40

20

40

60 80

100

female male

2001 2011

Female 40% Male

60%

Panel(b)

Male Female

50% 50%

Panel(c)



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10. Five people P, Q, R, S and T work in a bank. P and Q don’t like each other but have to

share an office till T gets a promotion and moves to the big office next to the garden. R,

who is currently sharing an office with T wants to move to the adjacent office with S, the

handsome new intern.

Given the floor plan, what is the current location of Q, R and T? [O = office, WR = Wash

room]

[Ans. C]

Manager Entry Teller 1 Teller 2

WR 01 P,Q

02 03 04 T R, S

Garden

( )


WR 01 P,Q

02 03 04 R S

Garden

( )

T


WR 01 P,Q

02 03 04 R, T S

Garden

( )


WR 01 P

02 03 04 R S

Garden

( )

Q

T



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Technical

Q.1 - Q.25 Carry One Mark each.

1. ∫ ∫

dxdy _____________

[Ans. *] Range 1 to 3

∫ ∫sinx

xdxdy

After changing the order of integration

∫ ∫sinx

xdydx

∫sinx

x

,y- dx

∫ sinxdx

,cosx-

,cos cos0-

, 1 1- 2

2. [

2 2 3 30 1 1 10 0 3 30 0 0 2

] number of distinct eigen values are _________________

[Ans. *] Range: 3 to 3

3. For an LTI system, bode plot is given the number of system poles and zeros N and N in

the frequency range 1Hz f 107Hz is

y x

y π

y 0 x π



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(A) 4,2

(B) 7,4

(C) 6,3

(D) 5,2

4. Find the period of the signal x(t) ____________

x(t) 1 2cos t 3sin2

3t 4 cos .

2t

4/

[Ans. *] Range: 12 to 12

Given

x(t) 1 2 cos t 3 sin(2

3t) 4 cos(

2t

4)

T L M (T , T , T )

T 2

2sec

T 2

.

/ 3 sec

T 2

2 4sec

T L M(2, 3, 4)

12sec

5. Which of the following is analytic function?

( ) 1

1 z

( ) lnz

( ) cosz

( ) e

[Ans. C]

(a) f(z)

, we see that at z=1

f(z) is not analytic function.

10

30μF V (t)

10

30μF V (t)

10

30μF V (t)

10

30μF V (t)

105

30μF V (t)

106

30μF V (t)

107

30μF V (t)

40d dec

30μF V (t)

40d dec

30μF V (t)

60d dec

30μF V (t)

20d dec

30μF V (t)

60d dec

30μF V (t)



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(b) f(z)=lnz

f(z)

1

2ln(x y ) ⏟

u

i tan .y

x/

⏟

v

u

x 1

2

1

x y (2x)

x

x y

v

y

1

1 .

/

1

x x

x y

So, u

x v

y 1st R equation is satisfied.

Now, u

y 1

2

1

x y (2y)

y

x y

And v

x

1

1 .

/ y

x y

x y

So, u

y v

x 2nd R equation is satisfied.

Let at x=0 and y=0, lnz is not analytic.

(c) cosz is analytic, everywhere in z-plane

(d) e is not analytic at z=0

6. Find the value of

1

2 j∮ (z

1

z)

dx

Where c: |z|=1

[Ans. *]Range: 0 to 0



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7. The following circuit represents which logic operation:

(A) XOR

(B) Latch

(C) X – NOR

(D) SRAM Latch

8. V is square wave with minimum and maximum value if 10 and 8. iode is equal and

R R 50 . The average value of V is ___________V. (correct up to 2 decimal point)

9. V is 10V square wave with T 4 msec R 500 and 10 F capacitor 1s initially

uncharged at t=0. Diode is ideal the capacitor voltage V at t 3 sec is ___________

VDD

R

8V

Voltage across

10

Voltage across

V

Voltage across

Voltage across

Voltage across

R

Voltage across

V

Voltage across

R

Voltage across



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10. For the given differential equation

x d y

dx 3x

dy

dx 3y 0, x 0

It is given that y(1)=1 and y(2)=14 then find the value of y(1.5).

11. In the circuit shown, if the frequency of the CIK signal is 12KHz, then the frequency of the

signal at Q2 will be ___________KHz.


12. Given a real impulse response h(n) whose z-transform is H(z). The function P(z) =H(z) .

H(1/z) has zero at

P(z) of total 4-zero’s which of the following plots represent it

correctly

10

Voltage across

10

Voltage across

V

Voltage across

Voltage across

Voltage across

𝐶

Voltage across

VC

Voltage across

𝐷

Voltage across

R

Voltage across

( )

Voltage across

z

30μF V (t)

2 j2

30μF V (t)

0.5 j0.5

30μF V (t)

2

l

R

30μF V (t)

0.5 j0.5

30μF V (t)

Im

30μF V (t

( )

Voltage across

0.5 j0.5

30μF V (t)

0.5 j0.5

30μF V (t)

Im

30μF V (t

0.5 j0.5

30μF V (t)

0.5 j0.5

30μF V (t)

z 1

30μF V (t)



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13. A standard CMOS inverter is designed with equal rise and fall times ( ). If the width

of the PMOS transistors in the invertor is increased, what would be the effect on the Low

Noise Margin(NM ) & the high Noise Margin (NM )?

(A) both NM NM increses

(B) NM increases NM decreses

(C) NM decreases NM increses

(D) No change in the noise margins

( )

Voltage across

Im

30μF V (t

1 j

30μF V (t)

1 j

30μF V (t)

z 1

30μF V (t)

( )

Voltage across

Im

30μF V (t

z 1

30μF V (t)



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14. In the circuit shown, what are the values of F for EN=0 and EN=1 respectively?

(A) Hi

(B) Hi-Z & D

(C) 0 & D

(D) 0 &1

[Ans. B]

15. Consider the 2 port resistive network shown in the figure. When an excitation of 5V is

applied across port1 and port 2 is shorted, the current through the short circuit at port 2 is

measured to be 1A (see in the figure(A)) now, if an excitation of 5V is applied at port2 and

port1 is short circuited(see in the figure (B)) what is the current through the short

circuited at port 1?

(A) 2.5A

(B) 1A

(C) 0.5A

(D) 2A

16. H(s)

( )( ) where x(t) u(t). Find the forced response of the system.

EN

F

VDD

1Ω

30μF V (t

2Ω

30μF V (t

RΩ

30μF V (t

Port2

30μF V (t)

Port1

30μF V (t)

( )

30μF V (t)

5V

30μF V (t

1Ω

30μF V (t

2Ω

30μF V (t

RΩ

30μF V (t

1

30μF V (t)

( )

30μF V (t)

5V

30μF V (t

1Ω

30μF V (t

2Ω

30μF V (t

RΩ

30μF V (t

?

30μF V (



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17. The figure shows the high frequency V curve of a MOS capacitor (at T 300 K) with

m 0V & no oxide charges. The flat band inversion & accumulation conditions are

represented respectively by the points

(A) P, Q, R

(B) Q, R, P

(C) R, P, Q

(D) Q, P, R

[Ans. B]

For C-V characteristics

P→ Accumulation Region

Q→ Flat band Region

R→ Inversion Region

18. The correct circuit representation of the structure shown in the figure is

R

Q P

0 Va

n

p

n n

E

E

( )



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19. Match the following lists

List-1 List-2 1. . P. O 2. E Q. S 3. . R.

4. H S. J D

(A) 1 P, 2 Q, 3 R, 4 S

(B) 1 Q, 2 R, 3 P, 4 S

(C) 1 Q, 2 P, 3 R, 4 S

(D) 1 P, 2 R, 3 Q, 4 S

E

( )

E

( )

E

( )



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Q.26 - Q.55 Carry Two Mark each.

26. Consider UFB system as shown in the figure with integral compensator k/s and OLTF.

G(s) 1

s 3s 2 whene k 0?

The ve value of k for which there are exactly 2 poles of UFB on j axis is __________

(correct up to 2 decimal place)

27. Find the TF of the system

( ) H(s) s 1

s s 1

( ) H(s) s 1

s s s 1

( ) H(s) s 1

s 2s s 1

( ) H(s) s 1

2s 1

28. Causal 2nd order system with TF G(s)

with unit step R(s)

as input , c(s) is

output, time by c(t) to reach 94% of steady state value lim c(t) is

(A) 4.5

(B) 3.89

(C) 2.81

(D) 5.25

29. V for NMOS PMOS 1V. All transistors have same r of 6M

Output resistance 6

.

/ 5, ( )

.

/ 10, gain of the circuit is

_________.[ignore channel length modulation and body bias].

x(s)

l

l

l

k s

l

G(s)

l

y(s)

l

x(s)

l

l

l

s

l

1 s

l

1 s

l

∑

l

∑

l

l

y(s)

l

l



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30. For the given differential equation

x d y

dx 3x

dy

dx 3y 0, x 0

It is given that y (1) =1 and y (2) =14 then find the value of y (1.5).

[Ans. *] Range: 4.5 to 6.5

Let x e

x d y

dx ( 1)y

d

dz

x dy

dx y

( 1)y 3 y 3y 0

( 3 3)y 0

( 4 3)y 0

The auxiliary equation is

m 4m 3 0

(m 1)(m 3) 0

m 1, m 3

y e e

y x x

Given y(1)=1; y(2)=14

1

14 8 2

On solving two equations

2, 1

y 2x x

y(1.5) 2(1.5) 1.5 5.25

31. alculate ∫ (xdy ydx)

C Where C is a curve shown in figure below.

VDD 4V

V u

V



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(A) 8

(B) 16 2

(C) 12

(D) 6 /2

[Ans. C]

32. The RC circuit shown below has a variable resistance R(t) given by the following

expression (R(t) R .1

/ for 0 t T where R 1 and 1F .We are also given

that T 3R and the source voltage is V 1V. If the current at time t 0 is 1A , then the

current I9t) in amperes at time t T 2 is __________(rounded off to 2 decimal places)

33. For the given circuit state diagram is ___________. When A=1 or 0 [0 and 1 are the output

states]

3

1

1 4 5

30μF V (t)

R(t)

30μF V (t)

t 0

30μF V (t)

I(t)

30μF V (t)

V

30μF V (

1

0 LK

𝟎 𝟏

𝟎 𝟎

𝟏

𝟏 ( )



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34. In a long channel EMOS L 10HM,W 10HM. Given the accepter concentration is

5 10 6 cm ⁄ and mobility of e is H 800cm V sec⁄ the concentration is

3.45 10 7 F cm and V is 0.7V. Find the saturation current, given E 11.9 with

V 5V.


I a ox(W

L) [(V V )

2]

800 3.45 10 7 10 (4.3

2)

0.8 3.45 (4.3)

2 m

51 m

2

25.5 m

35. The Responsivity R of photo detector with efficiency and wavelength is given by

𝟎 𝟏

𝟎

𝟏

𝟏 ( )

𝟎

𝟎 𝟏

𝟏

𝟏

𝟎 ( )

𝟎

𝟎 𝟏

𝟏

𝟏

𝟎 ( )

𝟎



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( ) R

1.24

( ) R 1.24

( ) R

1.24

( ) R 1.24

[Ans. A]

Direct formula, relating Responsivity and efficiency is

R (

1.24)

36. An ideal pin junction diode with 1 at T 300k. The magnitude of RB voltage to reach

75% of reverse saturation current __________ MV. (approximate 2 decimal place)

[Ans. *] Range: 14.43 to 14.44

I I (e( ) 1)

Given I 75% I 3

4I

3

4I I (e

) 1)

V V ln (7

4)

0.0144 V

14.438 mV

37. x(t) x(t) U(t)

y(t) cx(t) U(t)

Where 0 ,0, 0, 1-

Then to obtain H(s) 1

s 3s 2s 1

A=? , C=?

38. A single bit equally likely to be 0 and 1 is to be sent across AWGN channel with PSD, No 2⁄

binary signaling with 0 P(t)and 1 q(t) is used for transmission along with optimal

receiver that minimizes bit error probability. Let (b)and (t) form orthonormal set , if

p(t) (t) , q(t) (t). The probability of error is

P but if p(t) (t), q(t) √E (t) and probability of error is also P then E=?

(A) 2

(B) 1

(C) 0

(D) 3



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39. If E[2X+Y]=0, E[X+2Y]=33, then E[X]+E[Y]=_______________, where X and Y are random

variables.

40. A voicem(t) 5k to 15K,m(t) MW to get f 91 m(t)) cos 2 f t. f 600KHz.

F (t) is digitized and achieved. This is done by first sampling f(t) at 1.2 times Nyquist

frequency and quantized each sample using 256=level quantizes. Finally each sample

coded to K-bits, K minimum code for encoding. Then R in Mbps is__________.

[Ans. *] Range: 11.2 to 12.2

m(t) 5K to 15KHz

M f(t) (1 m(t)) cos 2 f t

where f 600KHz

f(t)sampled at 1.2 timed NR

sampling rate 1.2 ,2 fma -,fm fc fm-

1.2 2 615K

1476 sample sec

it is quantized using 256 level quantizes

L 256 2 K 8

it rate (R ) n f 8 1476 Kbps

11.808 Mbps.

41. If Z is exponential random variable where 1

F ( ) *1 e

0 x 0x 0

Where F ( ) is cumulative density function (CDF). Then find

P ( 2

1) _______________

42. If

.

/

, then family of curves for n 1 and n 1 respectively are

(A) Parabola, Circle

(B) Circle, Hyperbola

(C) Hyperbola, Parabola

(D) Hyperbola, Circle

43. In the circuit shown, if v(t) 2 sin(1000t) volts, R 1k and 1 F, then the steady

state current i(t) in milli amperes(MA)is



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(A) sin(100t) 3 cos(1000t)

(B) sin(1000t) cos(1000t)

(C) 3 sin(1000t) cos(1000t)

(D) 2 sin(1000t) 2 cos(1000t)

44. f(x) is a differentiable function on at of real number given that f( 1) 0 and f (x) 2

then which one of the following inequality is true?

(E) f(x) 2 x 1

(F) f(x) 2x

( ) f(x) 1

2 x

( ) f(x) 1

2 x 1

45. Given the signal x(n) e e

, the Impulse Response value are

h(0) 1, h(1) a, h(2) b and h(n) 0 for other values of n. The values of a and b for

which the output y(n) 0

(A) a 1, b 1

(B) a 0, b 1

(C) a 1, b 1

(D) a 0, b 1

[Ans. B]

Given

x(n) e

e

h(n) ∑*1, a, b+

The frequency of x(n)is

2

pply zT on

H(z) 1 az bz

~

~

Voltage across

Voltage across

v(t)

Voltage across

i(t)

Voltage across

R

Voltage across

R

Voltage across

Voltage across

Voltage across

Voltage across

R

Voltage across

h(n) *1, a, b+

x(n) y(n) 0



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For z e

H(e ) 1 a e be

where |H(e ) |a

2

|1 ae

be |

1 aj b

s y(n) 0 0

The above is satisfied for a=0, b=1

47. A random process is given by y(t) h(t)yx(t) z(t)where x(t) is a white noise with

constant power spectral density S (F) 5W Hz and h(t) is a filter which is defined by

H(f) 0.5 for 5 f 5 and z(t) is a stationary process which is uncorrelated with

x(t). Whose Power spectrum is give as

The power of process y(t) is __________ walts.

y(t) h(t) x(t) z(t)__________

x(t) WGN 5 (f) 5W Hz

h(t) H(f) 0.5 for 5 f 5

z(t) stationary power uncorrelated with x(t)

FT of is y 1H(t)1 (x(f)) 2(f)

PS of y(t) is

sy(F) y(F) H(f) (f) z(f) 2 H(f) x(f) z(f)

x(n ϕ ) y(n)

30μF V (t)

x(n)

Voltage across

(ω π 2⁄ )

Voltage across a

sinusoidal

Voltage across a

input

Voltage across

1 S (t)

5 5 t

5 5



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output power ∫ Sy

(5)

∫, H(f) (f) z(f) -at

∫ (1

2)

5f 1

2 10 1

5

4 10

10

2 17.5 walts

48. Complementary MOS (CMOS) inverter has a midpoint voltage V

as shown in figure.

The value of V 3V. CMOS is operating at a voltage of

. The values of

, V 0.7V, 40 , V 0.9 V. The ratio of .

/ to .

/

is

____________(3 decimal accuracy)

[Ans. *] Range: 0.224 to 0.226

Given VDD 3V

t V V 1.5

Both Transistors NMOS and PMOS are in saturation

ID ID

1

2 (

W

L) (V V )

1

2 (

W

L) .V V /

1

2 100 (

W

L) (1.5 0.7)

1

2 40 (

W

L) (1.5 0.9)

.

/

.

/

40

100 (0.6)

(0.8)

2

5 (6

8)

0.225

V V

V

V V V



ME-



ECE

25

49. In a rectangular waveguide with width W and height h, The ratio of cutoff frequency of

TE mode to TE mode is 1:2, the aspect ratio w:h=____________(accuracy up to 2-

decimals)

[Ans.*] Range: 1.72 to 1.74

50. The dispersion in rectangular waveguide k(w) √w w . If the group velocity

v 2 108, the phase velocity is ___________

51. Two copper wires and carry currents I and 2I in opposite direction as shown in the

figure. The distance of separation between wires is 4r. the magnitude of magnetic flux

density at a distance of r from is ____________

r



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