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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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