electronics and communications final · 2019-09-11 · (c) poly‐silicon gate patterning (d)...
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Exercise 3
1 The maximum value of the function f(x) = in(1 + x) ‐ x (where x > ‐1) occurs
at x = _____.
2 Which ONE of the following is a linear non‐homogeneous differential
equation, where x and y are the independent and dependent variables
respectively?
(A) xdy xy edx
−+ = (B) 0dy xydx
+ =
(C) ydy xy edx
−+ = (D) 0ydy xdx
−+ =
3 Match the application to appropriate numerical method.
Application Numerical |Method
P1: Numerical integration M1: Newton‐Raphson Method
P2: Solution to a transcendental
equation
M2: Runge‐Kutta Method
P3: Solution to a system of linear
equations
M3: Simpson’s 1/3‐rule
P4: Solution to a differential equation M4: Gauss Elimination Method
(A) P1—M3, P2—M2, P3—M4, P4—M1
(B) P1—M3, P2—M1, P3—M4, P4—M2
(C) P1—M4, P2—M1, P3—M3, P4—M2
(D) P1—M2, P2—M1, P3—M3, P4—M4
4 An unbiased coin is tossed an infinite number of times. The probability that
the fourth head appears at the tenth toss is
(A) 0.067 (B) 0.073 (C) 0.082 (D) 0.091
5 If z = xy ln (xy), then
(A) 0z zx yx y
∂ ∂+ =
∂ ∂ B)
z zy xx y
∂ ∂=
∂ ∂
(C) z zx yx y
∂ ∂=
∂ ∂ D) 0z zy x
x y∂ ∂
+ =∂ ∂
6. A series RC circuit is connected to a DC voltage source at time t = 0. The
relation between the source voltage VS, the resistance R, the capacitance C,
and the current i(t) is given below:
1( ) ( ) .t
oVs Ri t i u du
c= + ∫
Which one of the following represents the current i(t)?
(A) (B)
(C) (D)
7 In the figure shown, the value of the current I (in Amperes) is__________.
8. In MOSFET fabrication, the channel length is defined during the process of
(A) isolation oxide growth (B) channel stop implantation
(C) poly‐silicon gate patterning
(D) Lithography step leading to the contact pads
9. A thin P‐type silicon sample is uniformly illuminated with light which
generates excess carriers. The recombination rate is directly proportional to
(A) the minority carrier mobility
(B) the minority carrier recombination lifetime
(C) the majority carrier concentration
(D
10. A
K
11 T
(A
(B
(C
(D
12 In
A
D) the exce
At T = 300
KTq
= 26 m
The desirab
A) high inp
B) high inp
C) low inp
D) low inp
n the circu
Assume tha
ess minorit
K, the ho
mV. The ho
ble charact
put resista
put resista
ut resistan
put resistan
uit shown
at RB = 100
ty carrier c
le mobility
le diffusion
teristics of
nce and hi
nce and lo
nce and hig
nce and low
, the PNP
0 kΩ. For V
concentrat
y of a sem
n constant
a trans co
igh output
ow output
gh output
w output r
P transisto
V0 to be 5 V
tion
miconducto
t Dp in cm2/
nductance
resistance
resistance
resistance
resistance
r has |VB
V, the value
or μp = 50
/s is _____
e amplifier
e
E| = 0.7 V
e of RC (in k
0 cm2/V‐s
____
are
V and ß =
kΩ) is____
and
= 50.
____
13 T
st
_
14. A
c
_
15. T
(A
(C
The figure
teady‐stat
__________
An analog v
onversion
_________
The circuit s
A) Toggle F
C) SR Latch
shows a h
e current
___ .
voltage in
to 4‐bit di
shown in t
Flip Flop
h
half‐wave
(in Ampe
the range
igital outp
the figure i
(D) Ma
rectifier. T
eres) thro
e 0 to 8 V
ut. The ma
is a
(B) JK Flip
aster‐Slave
The diode
ough the
is divided
aximum qu
Flop
e D Flip Flo
D is idea
diode is
in 16 equa
uantization
op
l. The ave
approxima
al intervals
n error (in
rage
ately
s for
V) is
16. C
W
(A
(C
17. L
u
fr
(A
(C
18. F
If
(A
Consider th
Which one
A) F W=
C)F W =
et x(t) = c
sing an i
requency/f
A) 5 Hz and
C) 5 Hz, 10
or an all‐p
f Re(a) ≠ 0
A) a
he multiple
of the follo
1 2WS S
11 S + +
cos(10πt)
ideal low‐
frequencie
d 15 Hz on
0 Hz and 15
ass system
0, Im(a) ≠ 0
(B)a*
exer based
owing Boo
2S
+ cos(30π
‐pass filte
es present
ly
5 Hz only
m H(z) = ((1
z
0, then b eq
(C) 1/a
logic circu
olean funct
(B) F = WS
(D) F W=
t) be sam
er with cu
in the reco
(B)
(D)
)1
1)
z b
az
−
−
−
−, w
quals
a*
uit shown i
tions is rea
S1 + WS2 + S
1W SS⊕ ⊕
mpled at 2
ut‐off freq
onstructed
10 Hz and
5 Hz only
where |H (e
(D) 1/a
n the figur
alized by th
S1S2
2S
0 Hz and
quency of
d signal is/a
15 Hz only
e‐jω )| = 1, f
re.
he circuit?
reconstru
f 20 Hz.
are
y
for all ω.
cted
The
19. A
m
re
_
20. C
T
(A
(C
21. T
sy
th
22. T
A modulate
m(t) has f
equired ra
_______ .
Consider th
The transfe
A) 1 2
1 21G G
G G+
C) G1 G2 + G
The input ‐
ystem wit
hen the va
The phase r
ed signal i
frequency
ate (in kHz
he followin
er function
2
(B)
G2 + 1 (D
‐3e2t u(t),
h transfer
alue of the
response o
ϕ
s y(t) = m
compone
z) at which
g block dia
( )( )
C sR s
is
) G1 G2 + G
D) 1
1 21GG G+
where u(t
functionss
output at
of a pass ba
( ) 2fϕ π= −
(t)cos(400
ents less t
h y(t) shou
agram in th
G1 + 1
2
t) is the u
23
ss
−+
. If th
steady sta
and wavef
( )cf fπα −
00πt), wh
than 5 kH
uld be sam
he figure.
unit step f
he initial va
ate is
form at the
2 cfπβ−
ere the ba
Hz only. T
mpled to r
function, is
alue of the
e receiver i
aseband si
The minim
recover m(
s applied
e output i
is given by
ignal
mum
(t) is
to a
s ‐2,
y
w
a
(A
23. C
m
fr
(A
24. C
c
_
25. In
s
th
R
W
re
(A
where fc is
ctual signa
A) α βα β
−+
Consider a
maximum
requency f
A) β1 f1 + β
Consider an
m. For th
________.
n the follo
ignal via a
he charact
Rx are all re
Which one
eceived sig
A) The sig
the centr
al propagat
(B)
n FM sign
deviation
fc is
2 f2
n air filled
is wavegu
wing figur
coaxial ca
teristic imp
eal.
of the fol
gnal due to
nal gets di
e frequenc
tion delay
) αβ
α β+
nal f(t) = c
of the i
(B) β1
rectangula
ide, the c
e, the tran
able to the
pedance Z0
lowing sta
o impedan
storted if Z
cy, and α
from the t
(C)
cos[2πfc t +
nstantane
f2 + β2 f1
ar wavegui
cut‐off freq
nsmitter Tx
receiver R
0 of the ca
tements is
ce mismat
ZR ≠ Z0, irre
and β are
transmitte
α (
+ β2 sin 2
ous frequ
(C) β1 +
de with a c
quency (in
x sends a w
Rx. The out
ble and th
s TRUE abo
tch?
espective o
e positive c
r to
D) β
π f2 t] sin
uency from
+ β2 (D) f1
cross‐secti
n MHz) of
wideband
tput imped
he input im
out the dis
of the valu
constants.
n 2π f2 t].
m the ca
1 + f2
ion of 5 cm
f TE21 mod
modulate
dance ZT o
mpedance Z
stortion of
e of ZT
The
The
rrier
m × 3
de is
d RF
of Tx,
ZR of
f the
(B) The signal gets distorted if ZT ≠ Z0, irrespective of the value of ZR
(C) Signal distortion implies impedance mismatch at both ends: ZT ≠ Z0 and
ZR ≠ Z0
(D) Impedance mismatches do NOT result in signal distortion but reduce
power transfer efficiency
26 The maximum value of f(x) = 2x3 ‐ 9x2 + 12 x ‐3 in the interval 0 ≤ x ≤ 3
is_______.
27 Which one of the following statements is NOT true for a square matrix A?
(A) If A is upper triangular, the Eigen values of A are the diagonal
elements of it
(B) If A is real symmetric, the Eigen values of A are always real and
positive
(C) If A is real, the Eigen values of A and AT are always the same
(D) If all the principal minors of A are positive, all the eigen values of A
are also positive
28. A fair coin is tossed repeatedly till both head and tail appear at least once.
The average number of tosses required is______.
29. Let X1, X2, and X3 be independent and identically distributed random
variables with the uniform distribution on [0, 1]. The probability P{X1 + X2 ≤
X3} is ________ .
30. C
L
T
T
(A
31 In
Consider th
et C = 100
Two such b
The transfe
A) 1
ss+
n the circu
he building
µF and R =
locks are c
er function
(B)
it shown in
block calle
= 10 kΩ.
connected
3
1
( )( )
V sV s
of t
) 2
1 3ss s+ +
n the figur
ed ‘Netwo
in cascade
he cascade
2s (C)
e, the valu
ork N’ show
e, as show
ed networ
2
1s
s⎛ ⎞⎜ ⎟+⎝ ⎠
(
ue of node
wn in the fi
n in the fig
k is
D) 2
ss+
voltage V2
(A) 22 + j 2
(B) 2 + j 22
(C) 22 – j 2
(D) 2 – j 22
gure.
gure.
2 is
2 V
2 V
2 V
2 V
32. In
w
p
33. F
e
34. T
x
c
p
n the circu
which the
purely resis
or the Y‐
quivalent
The donor
1016 cm‐3
oncentrati
permittivity
uit shown
Norton eq
stive, is __
network s
Δ‐networ
and accep
and 5 × 10
ion in silico
y of silicon
in the fig
quivalent
________ .
shown in
k is ____.
ter impuri
018 cm‐3, re
on ni = 1.5
n ∈si = 1.0
gure, the a
impedanc
the figure
ties in an
espectively
5 × 1010 cm
4 × 10‐12F/
angular fre
e as seen
e, the val
abrupt jun
y. Assume
m‐3 at 300
/cm. The b
equency ω
n from ter
ue of R1
nction silico
that the i
K, KTq
= 2
built‐in pot
ω (in rad/s
rminals b‐
(in Ω) in
on diode a
ntrinsic ca
26 mV and
tential and
s), at
b' is
the
are 1
rrier
d the
d the
d
re
(A
(C
35 T
1
m
re
36 A
s
µ
8
d
o
37. In
V
(A
epletion
espectively
A) 0.7 V an
C) 0.7 V an
The slope o
10‐3Ω)‐1 at
modulation
egime is ap
An ideal MO
ubstrate. W
µm is form
8.854 x 10
ioxide are
oxide regio
n the circu
VCE(sat) = 0.2
A) For RC =
width of
y, are
nd 1 x 10‐4
nd 3.3 x 10
of the ID vs
VDS = 0.1
n, the slop
pproximat
OS capacit
When a ga
med with a
0‐14 F/cm
e 12 and 4
n is ______
uit shown,
2 V. Which
= 1 kΩ, the
the diod
cm
0‐5 cm
s. VGS curve
1 V. For t
e of the
ely ______
tor has bo
ate voltage
surface (c
and the r
4, respectiv
____.
, the silico
one of the
e BJT opera
de under
(B) 0.86 V
(D)
e of an n‐c
he same d
DI vs. VGS
____.
ron doping
e is applie
channel) p
relative pe
vely, the p
on BJT has
e following
ates in the
thermal
V and 1 x 1
0.86 V an
hannel MO
device, ne
S curve (in
g‐concentr
d, a deple
potential o
ermittivitie
peak electr
s ß = 50. A
g statemen
saturation
equilibriu
0‐4 cm
d 3.3 x 10‐
OSFET in li
eglecting c
√A/V) un
ration of 1
etion regio
of 0.2 V. G
es of silico
ric field (in
Assume VB
nts is correc
n region
m conditi
‐5 cm
near regim
channel le
der satura
015 cm‐3 in
n of width
Given that
on and sil
n V/µm) in
BE = 0.7 V
ct?
ions,
me is
ngth
ation
n the
h 0.5
ε0 =
licon
n the
and
(B
(C
(D
38. A
(A
(C
39 F
=
re
B) For RC =
C) For RC =
D) For RC =
Assuming t
A) 15 32
V V−
C) 132
V− +
or the MO
= 100 µA/V
egion to lin
= 3 kΩ, the
=20 kΩ, the
=20 kΩ, th
hat the Op
2V
272
V
OSFET M1 s
V2 and VTH
near region
e BJT opera
e BJT oper
e BJT oper
p‐amp in th
shown in th
= 0.5 V. T
n when Vin
ates in the
rates in the
rates in the
he circuit s
(B) 1522
V −
(D) 13V− +
he figure, a
The transi
n (in Volts)
saturation
e cut‐off re
e linear reg
shown is id
252
V
2112
V+
assume W
stor M1 s
is _______
n region
egion
gion
deal, Vo is g
W/L = 2, VDD
witches fr
____ .
given by
D = 2.0 V, μ
rom satura
μn Cox
ation
40. If
(A
(C
41. In
is
f WL is the
A)
C)
n the circu
s given by
Word Line
it shown, W
e and BL th
W and Y ar
he Bit Line,
(B)
(D)
re MSBs of
, an SRAM
f the contr
cell is sho
rol inputs. T
wn in
The outpu
t F
(A) F WX WX YZ= + + (B) F WX WX YZ= + +
(C) F WXY WXY = + (D) ( )F W X YZ= +
42. If X and Y are inputs and the Difference (D = X – Y) and the Borrow (B) are
the outputs, which one of the following diagrams implements a half‐
subtractor?
(A) (B)
(C) (D)
43. Let H1 (z) = 1 – pz‐1)‐1, H2(z) = 1 – qz
‐1)‐1, H(z) = H1(z) + r H2(z). The quantities
p, q, r are real numbers. Consider p = 1/2 , q = 1 – ¼ |r| <1. If the zero of
H(Z) lies on the unit circle, then r = ______
44. L
fu
S
S
S
F
(A
(C
45. T
re
46. T
47. T
et h(t) de
unction s
1: The syst
2: ( )1
( )h t
h t+
3: A non‐c
or the abo
A) only S1
C) only S1
The z‐trans
egion of co
The state e
The state e
enote the
11+. Consi
tem is stab
)is indepen
ausal syste
ove system
and S2 are
and S3 are
form of th
onvergence
quation of
quation of
impulse r
der the fo
ble.
ndent of t
em with th
m,
e true
e true
he sequenc
e |z| > 2. T
f a second‐
f a second‐
x(t) = Ax
response o
llowing thr
for t > 0.
he same tra
ce x[n] is g
Then, x [2]
‐order line
‐order line
x(t), x(0)
of a causa
ree statem
ansfer func
(B) only S
(D) S1, S2
given by X[
is_______
ar system
ar system
) = x0
al system
ments.
ction is sta
S2 and S3 a
2 and S3 ar
z] = (
1
1 2z−
__
is given by
is given by
with tran
able.
are true
re true
)21
1
z−,with
y
y
nsfer
h the
F
W
(A
(C
48. In
a
h
(A
(C
49. L
s
s
or x0 = 11−⎡⎣
When 0x =
A) 8 118 22
t
te
e e
−
−− +
−⎡⎢⎣
C) 23 5
3 10
t
te e
e
− −
−−
− +⎡⎢⎣
n the root
rrows hav
has this roo
A) ( 2)(s s+
C) ( 7)(
ss s+
et X(t) be
pectral de
pectral de
[, ( ) ex t ⎡⎤ =⎦ ⎢⎣
35 , ( )x t⎡ ⎤⎣ ⎦ is
2
2
t
te
e
−
−⎤⎥⎦
2
2
t
te−⎤⎥⎦
t locus plo
ve been re
ot locus?
14)( 7
ss s
++ +
72)( 4
ss s
++ +
e a wide s
ensity Y(t)
nsity SY(f) i
[ ]and
t
te
e
−
−−⎤⎥⎦
s
ot shown
moved. W
7)
4)
sense stat
is the pro
is
0for x ⎡= ⎣
(B) 11 811
t
te
e
−
−−
− +⎡⎢⎣
(D) 5 35
t
te
e
−
−−
− −⎡⎢⎣
in the figu
Which one o
(B) ( 1)s +
(D) ( 1)( 7)ss
++
tionary (W
ocess defin
01 , ( ) e
ex t
−
−⎡⎤⎦ ⎢⎣
2
28
16
t
te
e
−
−+⎤⎥⎦
2
26
t
te
e
−
−−⎤⎥⎦
ure, the p
of the follo
4( 2)(ss s
++ +
)( 2))( 4)
ss
++
WSS) rando
ned as Y(t)
2
22
t t
t te
e e
− −
− −−
+⎤⎥⎦
ole/zero m
owing tran
7)
om proces
) = X(2t ‐
marks and
nsfer funct
ss with po
1), the po
the
tions
ower
ower
(A
(C
50. A
d
S
w
c
fi
T
51. In
a
st
se
52. A
in
(B
ra
A) ( )ys f =
C) (ys f
A real ban
ensity
1( )XS f⎧
= ⎨⎩
where f is t
os 16000 π
ilter of uni
The output
n a PCM sy
t the Nyqu
tep size 0
econd is__
A binary ra
nput to a
BSCs) each
andom var
12 2X
fS ⎛= ⎜⎝
1)2 X
ff S ⎛= ⎜⎝
nd‐limited
60 (30000
− −
he frequen
πt and the
ty gain wit
power (in
ystem, the
uist rate. T
.75 V. The
____.
andom var
cascade o
h with cro
riables Y1 a
j fe π−⎞⎟⎠
2f ⎞
⎟⎠
random p
| |) Wattf−
ncy expres
e resultant
th centre f
Watts) is_
signal m(t
The sample
e minimum
iable X tak
of 2 indepe
ossover pr
and Y2 as s
(B)
(D)
process X(
for |ts /ot
Hz
ssed in Hz.
signal is p
frequency
_______.
t) = {sin(10
es are proc
m data rat
kes the va
endent ide
robability
shown in t
1( )2ys f =
1( )2ys f =
(t) has tw
| 3KHztherwisef ≤
The signal
passed thr
of 8 kHz a
0077πt) + c
cessed by a
te of the
alue of 1 w
entical bin
1/2. The
he figure.
2XfS e−⎛ ⎞
⎜ ⎟⎝ ⎠
2XfS e−⎛ ⎞
⎜ ⎟⎝ ⎠
wo‐sided p
z
l X(t) modu
ough an id
and band‐w
cos(100πt)
a uniform
PCM syste
with proba
nary symm
output of
/2j fπ
2j fπ−
power spe
ulates a ca
deal band‐
width of 2
)} V is sam
quantizer
em in bits
ability 1/3.
metric chan
BSCs are
ctral
rrier
pass
kHz.
pled
with
per
X is
nnels
the
T
53 G
u
is
54. A
s
a
c
(A
m
(
(C
(D
55. A
E
re
tr
The value o
Given the v
nit vector
s________
A region sh
urface cur
mperes pe
onductor i
A) ( ˆ ˆx z+
meter
(B) x2Amp
C) z2− Am
D) z2Amp
Assume t
10cos(E ω=
elative pe
ransmissio
of H(Y1) + H
vector A = (
s along x,
_
own below
rrent sK o
er meter. T
is
)z 2 Ampe
peres per m
peres per
eres per m
that a
3 3 3 )t x zω
ermittivity
on in the di
H(Y2) in bits
(cos x)(sin
y directio
w contains
on the sur
The tangen
eres per
meter
meter
meter
plane w
ˆ) ya V/m is
3 which
ielectric sla
s is_______
y) ˆxa + (sin
ns, respec
a perfect
rface of t
ntial H fie
wave in
incident o
covers t
ab is_____
_________
x)(cos y) a
tively. The
conductin
the perfec
eld in the a
air wit
n a non‐m
he region
____ degre
___
ˆya , where
e magnitud
g half‐spac
ct conduct
air just abo
th an e
magnetic di
n z > 0.
ees.
ˆxa , ˆya de
de of curl
ce and air.
tor is sK =
ove the per
electric
electric sla
The angle
note
of A
The
ˆ2x=
rfect
field
ab of
e of
Key for Exercise‐3
Q. No. Key 1 ‐0.01 to 0.01 2 A 3 B 4 C 5 C 6 A 7 0.49 to 0.51 8 C 9 D 10 12.9 to 13.1 11 A 12 1.04 to 1.12 13 0.08 to 0.12 14 0.24 to 0.26 15 D 16 D 17 A 18 B 19 9.5 to 10.5 20 C 21 ‐0.01 to 0.01 22 C 23 A 24 7750 to 7850 25 C 26 5.9 to 6.1 27 B 28 2.9 to 3.1
29 0.15 to 0.18 30 B 31 D 32 1.9 to 2.1 33 9 to 11 34 D 35 0.06 to 0.08 36 2.3 to 2.5 37 B 38 D 39 1.4 to 1.6 40 B 41 C 42 A 43 ‐0.6 to ‐0.4 44 A 45 11.9 to 12.1 46 0.49 to 0.51 47 B 48 B 49 C 50 2.4 to 2.6 51 199 to 201 52 1.9 to 2.1 53 ‐0.01 to 0.01 54 D 55 29 to 31
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