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Page 1
Transmission Lines
1. A load impedance, (200 + j0) O is to be matched to a 50 O lossless
transmission line by using a quarter wave line transformer (QWT). The
characteristic impedance of the QWT required is _________
[GATE 1994: 1 Mark]
Soln. For Quarter wave line transformer
?? ?? ?? = ?? ????
. ?? ??
?? ?? ?? = ???? × ??????
?? ?? = ?????? ??
2. A lossless transmission line having 50 O characteristic impedance and
length ?? 4 / is short circuited at one end and connected to an ideal voltage
source of 1V at the other end. The current drawn from the voltage sources
is
(a) 0
(b) 0.02 A
(c) 8
(d) None of the these
[GATE 1996: 1 Mark]
Soln. For quarter wave transformer ( ?? 4 / )
?? ????
=
?? ?? ?? ?? ??
?? ?? = ?? (short circuit)
?? ????
=
?? ?? ?? ?? = 8 (open circuit)
The current drawn from the voltage source ?? ?? =
?? ?? ?? ????
=
?? ?? 8
= ??
Option (a)
3. The capacitance per unit length and the characteristic impedance of a
lossless transmission line are C and Z
0
respectively. The velocity of a
travelling wave on the transmission line is
Page 2
Transmission Lines
1. A load impedance, (200 + j0) O is to be matched to a 50 O lossless
transmission line by using a quarter wave line transformer (QWT). The
characteristic impedance of the QWT required is _________
[GATE 1994: 1 Mark]
Soln. For Quarter wave line transformer
?? ?? ?? = ?? ????
. ?? ??
?? ?? ?? = ???? × ??????
?? ?? = ?????? ??
2. A lossless transmission line having 50 O characteristic impedance and
length ?? 4 / is short circuited at one end and connected to an ideal voltage
source of 1V at the other end. The current drawn from the voltage sources
is
(a) 0
(b) 0.02 A
(c) 8
(d) None of the these
[GATE 1996: 1 Mark]
Soln. For quarter wave transformer ( ?? 4 / )
?? ????
=
?? ?? ?? ?? ??
?? ?? = ?? (short circuit)
?? ????
=
?? ?? ?? ?? = 8 (open circuit)
The current drawn from the voltage source ?? ?? =
?? ?? ?? ????
=
?? ?? 8
= ??
Option (a)
3. The capacitance per unit length and the characteristic impedance of a
lossless transmission line are C and Z
0
respectively. The velocity of a
travelling wave on the transmission line is
(a) Z
0
C
(b) 1/(Z
0
C)
(c) Z
0
/C
(d) C/Z
0
[GATE 1996: 1 Mark]
Soln. ?? ?? = v
?? ?? , ?? ?? ?? =
?? ??
???????????????? ( ?? )=
?? v ????
=
?? v( ?? ?? ?? ?? ) ( ?? )
=
?? ?? ?? ??
Option (b)
4. A transmission line of 50 O characteristic impedance is terminated with a
100 O resistance. The minimum impedance measured on the line is equal
to
(a) 0 O
(b) 25 O
(c) 50 O
(d) 100 O
[GATE 1997: 1 Mark]
Soln. ?? ?? = ???? ??
?? ?? = ?????? ??
?? ?? > ?? ??
?? ???? ( ?????? )
=
?? ?? ?? ?? ??
=
???? ×????
?????? = ???? ??
Option (b)
5. All transmission line section in Figure, have a characteristic impedance
R
0
+ j0. The input impedance Z
in
equals
Page 3
Transmission Lines
1. A load impedance, (200 + j0) O is to be matched to a 50 O lossless
transmission line by using a quarter wave line transformer (QWT). The
characteristic impedance of the QWT required is _________
[GATE 1994: 1 Mark]
Soln. For Quarter wave line transformer
?? ?? ?? = ?? ????
. ?? ??
?? ?? ?? = ???? × ??????
?? ?? = ?????? ??
2. A lossless transmission line having 50 O characteristic impedance and
length ?? 4 / is short circuited at one end and connected to an ideal voltage
source of 1V at the other end. The current drawn from the voltage sources
is
(a) 0
(b) 0.02 A
(c) 8
(d) None of the these
[GATE 1996: 1 Mark]
Soln. For quarter wave transformer ( ?? 4 / )
?? ????
=
?? ?? ?? ?? ??
?? ?? = ?? (short circuit)
?? ????
=
?? ?? ?? ?? = 8 (open circuit)
The current drawn from the voltage source ?? ?? =
?? ?? ?? ????
=
?? ?? 8
= ??
Option (a)
3. The capacitance per unit length and the characteristic impedance of a
lossless transmission line are C and Z
0
respectively. The velocity of a
travelling wave on the transmission line is
(a) Z
0
C
(b) 1/(Z
0
C)
(c) Z
0
/C
(d) C/Z
0
[GATE 1996: 1 Mark]
Soln. ?? ?? = v
?? ?? , ?? ?? ?? =
?? ??
???????????????? ( ?? )=
?? v ????
=
?? v( ?? ?? ?? ?? ) ( ?? )
=
?? ?? ?? ??
Option (b)
4. A transmission line of 50 O characteristic impedance is terminated with a
100 O resistance. The minimum impedance measured on the line is equal
to
(a) 0 O
(b) 25 O
(c) 50 O
(d) 100 O
[GATE 1997: 1 Mark]
Soln. ?? ?? = ???? ??
?? ?? = ?????? ??
?? ?? > ?? ??
?? ???? ( ?????? )
=
?? ?? ?? ?? ??
=
???? ×????
?????? = ???? ??
Option (b)
5. All transmission line section in Figure, have a characteristic impedance
R
0
+ j0. The input impedance Z
in
equals
?? ?? / ?? ?? /
?? ?? ??
?? ?? /??
?? ?? /
?? ?? ??
(a)
2
3
?? 0
(b) ?? 0
(c)
3
2
?? 0
(d) 2 ?? 0
[GATE 1998: 1 Mark]
Soln. For ?? ?? / line, ?? ?? ?? ?? =
?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? /
= ?? ?? ??
For ?? ?? / line, ?? ?? ?? ?? = ?? ?? ?? = ????
??
For ?? ?? / line, ?? ?? = ( ????
?? )? ?? ?? ??
= ?? ??
For transmission line of length ?? , ?? ????
= ?? ?? [
?? ?? +?? ?? ?? ?????? ?? ?? ?? ?? +?? ?? ?? ?????? ?? ?? ]
?? = ?? ?? / , ?? ????
= ?? ?? [
?? ?? + ?? ?? ?? ?? ?? + ?? ?? ?? ]
?? ????
= ?? ?? [
?? ?? +?? ?? ?? ?? ?? +?? ?? ?? ] = ?? ??
Option (b)
6. The magnitudes of the open – circuit and short – circuit input impedances
of a transmission line are 100 O and 25 O respectively. The characteristic
impedance of the line is.
Page 4
Transmission Lines
1. A load impedance, (200 + j0) O is to be matched to a 50 O lossless
transmission line by using a quarter wave line transformer (QWT). The
characteristic impedance of the QWT required is _________
[GATE 1994: 1 Mark]
Soln. For Quarter wave line transformer
?? ?? ?? = ?? ????
. ?? ??
?? ?? ?? = ???? × ??????
?? ?? = ?????? ??
2. A lossless transmission line having 50 O characteristic impedance and
length ?? 4 / is short circuited at one end and connected to an ideal voltage
source of 1V at the other end. The current drawn from the voltage sources
is
(a) 0
(b) 0.02 A
(c) 8
(d) None of the these
[GATE 1996: 1 Mark]
Soln. For quarter wave transformer ( ?? 4 / )
?? ????
=
?? ?? ?? ?? ??
?? ?? = ?? (short circuit)
?? ????
=
?? ?? ?? ?? = 8 (open circuit)
The current drawn from the voltage source ?? ?? =
?? ?? ?? ????
=
?? ?? 8
= ??
Option (a)
3. The capacitance per unit length and the characteristic impedance of a
lossless transmission line are C and Z
0
respectively. The velocity of a
travelling wave on the transmission line is
(a) Z
0
C
(b) 1/(Z
0
C)
(c) Z
0
/C
(d) C/Z
0
[GATE 1996: 1 Mark]
Soln. ?? ?? = v
?? ?? , ?? ?? ?? =
?? ??
???????????????? ( ?? )=
?? v ????
=
?? v( ?? ?? ?? ?? ) ( ?? )
=
?? ?? ?? ??
Option (b)
4. A transmission line of 50 O characteristic impedance is terminated with a
100 O resistance. The minimum impedance measured on the line is equal
to
(a) 0 O
(b) 25 O
(c) 50 O
(d) 100 O
[GATE 1997: 1 Mark]
Soln. ?? ?? = ???? ??
?? ?? = ?????? ??
?? ?? > ?? ??
?? ???? ( ?????? )
=
?? ?? ?? ?? ??
=
???? ×????
?????? = ???? ??
Option (b)
5. All transmission line section in Figure, have a characteristic impedance
R
0
+ j0. The input impedance Z
in
equals
?? ?? / ?? ?? /
?? ?? ??
?? ?? /??
?? ?? /
?? ?? ??
(a)
2
3
?? 0
(b) ?? 0
(c)
3
2
?? 0
(d) 2 ?? 0
[GATE 1998: 1 Mark]
Soln. For ?? ?? / line, ?? ?? ?? ?? =
?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? /
= ?? ?? ??
For ?? ?? / line, ?? ?? ?? ?? = ?? ?? ?? = ????
??
For ?? ?? / line, ?? ?? = ( ????
?? )? ?? ?? ??
= ?? ??
For transmission line of length ?? , ?? ????
= ?? ?? [
?? ?? +?? ?? ?? ?????? ?? ?? ?? ?? +?? ?? ?? ?????? ?? ?? ]
?? = ?? ?? / , ?? ????
= ?? ?? [
?? ?? + ?? ?? ?? ?? ?? + ?? ?? ?? ]
?? ????
= ?? ?? [
?? ?? +?? ?? ?? ?? ?? +?? ?? ?? ] = ?? ??
Option (b)
6. The magnitudes of the open – circuit and short – circuit input impedances
of a transmission line are 100 O and 25 O respectively. The characteristic
impedance of the line is.
(a) 25 O
(b) 50 O
(c) 75 O
(d) 100 O
[GATE 2000: 1 Mark]
Soln. ?? ?? = v?? ????
. ?? ????
= v?????? × ????
?? ?? = ???? × ??
= ???? ??
Option (b)
7. A transmission line is distortion less if
(a) ???? =
1
????
(b) ???? = ????
(c) ???? = ????
(d) ???? = ????
[GATE 2001: 1 Mark]
Soln. For a distortion less line, velocity of propagation ?? =
?? ?? must be
independent of frequency. To achieve this
???? = ????
????
?? ?? =
?? ??
Option (c)
8. The VSWR can have any value between
(a) 0 and 1
(b) – 1 and + 1
(c) 0 and 8
(d) 1 and 8
[GATE 2002: 1 Mark]
Soln. ???????? =
?? +|?? |
?? -|?? |
Where ?? is reflection coefficient ?? can take values between 0 and 1
when ?? = ?? , ???????? = ??
?? = ?? , ???????? = 8
Option (d)
Page 5
Transmission Lines
1. A load impedance, (200 + j0) O is to be matched to a 50 O lossless
transmission line by using a quarter wave line transformer (QWT). The
characteristic impedance of the QWT required is _________
[GATE 1994: 1 Mark]
Soln. For Quarter wave line transformer
?? ?? ?? = ?? ????
. ?? ??
?? ?? ?? = ???? × ??????
?? ?? = ?????? ??
2. A lossless transmission line having 50 O characteristic impedance and
length ?? 4 / is short circuited at one end and connected to an ideal voltage
source of 1V at the other end. The current drawn from the voltage sources
is
(a) 0
(b) 0.02 A
(c) 8
(d) None of the these
[GATE 1996: 1 Mark]
Soln. For quarter wave transformer ( ?? 4 / )
?? ????
=
?? ?? ?? ?? ??
?? ?? = ?? (short circuit)
?? ????
=
?? ?? ?? ?? = 8 (open circuit)
The current drawn from the voltage source ?? ?? =
?? ?? ?? ????
=
?? ?? 8
= ??
Option (a)
3. The capacitance per unit length and the characteristic impedance of a
lossless transmission line are C and Z
0
respectively. The velocity of a
travelling wave on the transmission line is
(a) Z
0
C
(b) 1/(Z
0
C)
(c) Z
0
/C
(d) C/Z
0
[GATE 1996: 1 Mark]
Soln. ?? ?? = v
?? ?? , ?? ?? ?? =
?? ??
???????????????? ( ?? )=
?? v ????
=
?? v( ?? ?? ?? ?? ) ( ?? )
=
?? ?? ?? ??
Option (b)
4. A transmission line of 50 O characteristic impedance is terminated with a
100 O resistance. The minimum impedance measured on the line is equal
to
(a) 0 O
(b) 25 O
(c) 50 O
(d) 100 O
[GATE 1997: 1 Mark]
Soln. ?? ?? = ???? ??
?? ?? = ?????? ??
?? ?? > ?? ??
?? ???? ( ?????? )
=
?? ?? ?? ?? ??
=
???? ×????
?????? = ???? ??
Option (b)
5. All transmission line section in Figure, have a characteristic impedance
R
0
+ j0. The input impedance Z
in
equals
?? ?? / ?? ?? /
?? ?? ??
?? ?? /??
?? ?? /
?? ?? ??
(a)
2
3
?? 0
(b) ?? 0
(c)
3
2
?? 0
(d) 2 ?? 0
[GATE 1998: 1 Mark]
Soln. For ?? ?? / line, ?? ?? ?? ?? =
?? ?? ?? ?? ?? =
?? ?? ?? ?? ?? ?? /
= ?? ?? ??
For ?? ?? / line, ?? ?? ?? ?? = ?? ?? ?? = ????
??
For ?? ?? / line, ?? ?? = ( ????
?? )? ?? ?? ??
= ?? ??
For transmission line of length ?? , ?? ????
= ?? ?? [
?? ?? +?? ?? ?? ?????? ?? ?? ?? ?? +?? ?? ?? ?????? ?? ?? ]
?? = ?? ?? / , ?? ????
= ?? ?? [
?? ?? + ?? ?? ?? ?? ?? + ?? ?? ?? ]
?? ????
= ?? ?? [
?? ?? +?? ?? ?? ?? ?? +?? ?? ?? ] = ?? ??
Option (b)
6. The magnitudes of the open – circuit and short – circuit input impedances
of a transmission line are 100 O and 25 O respectively. The characteristic
impedance of the line is.
(a) 25 O
(b) 50 O
(c) 75 O
(d) 100 O
[GATE 2000: 1 Mark]
Soln. ?? ?? = v?? ????
. ?? ????
= v?????? × ????
?? ?? = ???? × ??
= ???? ??
Option (b)
7. A transmission line is distortion less if
(a) ???? =
1
????
(b) ???? = ????
(c) ???? = ????
(d) ???? = ????
[GATE 2001: 1 Mark]
Soln. For a distortion less line, velocity of propagation ?? =
?? ?? must be
independent of frequency. To achieve this
???? = ????
????
?? ?? =
?? ??
Option (c)
8. The VSWR can have any value between
(a) 0 and 1
(b) – 1 and + 1
(c) 0 and 8
(d) 1 and 8
[GATE 2002: 1 Mark]
Soln. ???????? =
?? +|?? |
?? -|?? |
Where ?? is reflection coefficient ?? can take values between 0 and 1
when ?? = ?? , ???????? = ??
?? = ?? , ???????? = 8
Option (d)
9. A transmission line has a characteristic impedance of 50O and a
resistance of 0.1 O/m. If the line is distortion less, the attenuation
constant (in Np/m) is
(a) 500
(b) 5
(c) 0.014
(d) 0.002
[GATE 2010: 1 Mark]
Soln. Attenuation constant a to be independent of frequency for distortion
less transmission ?? = v ????
For distortion less transmission:
?? ?? =
?? ??
?? ?? = v
?? ?? = v
?? ??
?? = v???? = v ?? v ?? ?? ??
=
?? ?? ??
=
?? . ?? ????
= ?? . ?????? ???? ?? /
Option (d)
10. A transmission line of characteristic impedance 50O is terminated by a
50O 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 p/4 radians. The phase velocity of the wave along the line is
(a) 0.8 × 10
8
?? /??
(b) 1.2 × 10
8
?? /??
(c) 1.6 × 10
8
?? /??
(d) 3 × 10
8
?? /??
[GATE 2011: 1 Mark]
Soln. Phase difference ???? =
????
?? ???????? ????????????????????
?? ?? =
????
?? ( ?? × ????
-?? )
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