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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
2
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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ECE
3
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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ECE
4
(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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ECE
5
(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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ECE
6
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
( )
Manager Entry Teller 1 Teller 2
WR 01 P,Q
02 03 04 R S
Garden
( )
T
Manager Entry Teller 1 Teller 2
WR 01 P,Q
02 03 04 R, T S
Garden
( )
Manager Entry Teller 1 Teller 2
WR 01 P
02 03 04 R S
Garden
( )
Q
T
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ECE
7
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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ECE
8
(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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ECE
9
(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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ECE
10
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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ECE
11
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.
[Ans. *]Range: 4 to 4
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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ECE
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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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ECE
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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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ECE
14
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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ECE
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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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ECE
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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.
[Ans. *]Range: 25 to 26
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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ECE
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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
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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