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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 ???? = ???? ?? ???????? ???????????????????? ?? ?? = ???? ?? ( ?? × ???? -?? )Read More
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