Page 1 GATE EC - 1999 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 â€“ 1.25) of ONE mark each. For each of these sub-questions, four possible alternatives (A,B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answers in the boxes corresponding to the questions only on the FIRST sheet of the answer book. 1.1 Identify which of the following is NOT a true of the graph shown in Fig.P1.1 (a) begh (b) defg (c) adfg (d) aegh 1.2 The z-transform F(z) of the function ( ) nT f nT a = is (a) T z z a - (b) T z z a + (c) T z z a - - (d) T z z a - + 1.3 If ( ) ( ) ( ) , then f t F s f t T ? ? ? ? = - ? ? ? ? is equal to (a) ( ) sT e F s (b) ( ) sT e F s - (c) ( ) 1 sT F s e + (d) ( ) 1 sT F s e - - 1.4 A 2-port network is shown in Fig.P1.4. the parameter 21 h for this network can be given by (a) 1 2 - (b) 1 2 + (c) 3 2 - (d) 3 2 + 1.5 The early effect in a bipolar junction transistor is caused by (a) fast turn-on (b) fast turn-off (c) large collector-base reverse bias (d) large emitter-base forward bias 1 2 3 4 5 a b c d e f g h V 1 10µF + V 2 R R R I 1 I 2 - + - Page 2 GATE EC - 1999 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 â€“ 1.25) of ONE mark each. For each of these sub-questions, four possible alternatives (A,B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answers in the boxes corresponding to the questions only on the FIRST sheet of the answer book. 1.1 Identify which of the following is NOT a true of the graph shown in Fig.P1.1 (a) begh (b) defg (c) adfg (d) aegh 1.2 The z-transform F(z) of the function ( ) nT f nT a = is (a) T z z a - (b) T z z a + (c) T z z a - - (d) T z z a - + 1.3 If ( ) ( ) ( ) , then f t F s f t T ? ? ? ? = - ? ? ? ? is equal to (a) ( ) sT e F s (b) ( ) sT e F s - (c) ( ) 1 sT F s e + (d) ( ) 1 sT F s e - - 1.4 A 2-port network is shown in Fig.P1.4. the parameter 21 h for this network can be given by (a) 1 2 - (b) 1 2 + (c) 3 2 - (d) 3 2 + 1.5 The early effect in a bipolar junction transistor is caused by (a) fast turn-on (b) fast turn-off (c) large collector-base reverse bias (d) large emitter-base forward bias 1 2 3 4 5 a b c d e f g h V 1 10µF + V 2 R R R I 1 I 2 - + - GATE EC - 1999 1.6 The first dominant pole encountered in the frequency response of a compensated op-amp is approximately at (a) 5 Hz (b) 10 kHz (c) 1 MHz (d) 100 MHz 1.7 Negative feedback in an amplifier (a) reduces gain (b) increases frequency and phase distortions (c) reduces bandwidth (d) increase noise 1.8 In the cascade amplifier shown in Fig.P1.8, if the common-emitter stage(Q 1 ) has a transconductance 1 , m g and the common base stage (Q 2 ) has a transconductance 2 , m g then the overall transconductance o i i g v ? ? = ? ? ? ? of the cascade amplifier is (a) 1 m g (b) 2 m g (c) 1 2 m g (d) 2 2 m g 1.9 Crossover distortion behaviour is characteristic of (a) Class A output stage (b) Class B output stage (c) Class AB output stage (d) Common-base output stage 1.10 The logical expression y A AB = + is equivalent to (a) y AB = (b) y AB = (c) y A B = + (d) y A B = + 1.11 A Darlington emitter-follower circuit is sometimes used in the output stage of a TTL gate in order to (a) increase its I OL (b) reduces its I OH (c) increases its speed of operation (d) reduce power dissipation 1.12 Commercially available ECL gears use two ground lines and one negative supply in order to (a) reduce power dissipation (b) increase fan-out (c) reduce loading effect (d) eliminate the effect of power line glitches or the biasing circuit V i V o Q 2 Q 1 R L i o Page 3 GATE EC - 1999 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 â€“ 1.25) of ONE mark each. For each of these sub-questions, four possible alternatives (A,B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answers in the boxes corresponding to the questions only on the FIRST sheet of the answer book. 1.1 Identify which of the following is NOT a true of the graph shown in Fig.P1.1 (a) begh (b) defg (c) adfg (d) aegh 1.2 The z-transform F(z) of the function ( ) nT f nT a = is (a) T z z a - (b) T z z a + (c) T z z a - - (d) T z z a - + 1.3 If ( ) ( ) ( ) , then f t F s f t T ? ? ? ? = - ? ? ? ? is equal to (a) ( ) sT e F s (b) ( ) sT e F s - (c) ( ) 1 sT F s e + (d) ( ) 1 sT F s e - - 1.4 A 2-port network is shown in Fig.P1.4. the parameter 21 h for this network can be given by (a) 1 2 - (b) 1 2 + (c) 3 2 - (d) 3 2 + 1.5 The early effect in a bipolar junction transistor is caused by (a) fast turn-on (b) fast turn-off (c) large collector-base reverse bias (d) large emitter-base forward bias 1 2 3 4 5 a b c d e f g h V 1 10µF + V 2 R R R I 1 I 2 - + - GATE EC - 1999 1.6 The first dominant pole encountered in the frequency response of a compensated op-amp is approximately at (a) 5 Hz (b) 10 kHz (c) 1 MHz (d) 100 MHz 1.7 Negative feedback in an amplifier (a) reduces gain (b) increases frequency and phase distortions (c) reduces bandwidth (d) increase noise 1.8 In the cascade amplifier shown in Fig.P1.8, if the common-emitter stage(Q 1 ) has a transconductance 1 , m g and the common base stage (Q 2 ) has a transconductance 2 , m g then the overall transconductance o i i g v ? ? = ? ? ? ? of the cascade amplifier is (a) 1 m g (b) 2 m g (c) 1 2 m g (d) 2 2 m g 1.9 Crossover distortion behaviour is characteristic of (a) Class A output stage (b) Class B output stage (c) Class AB output stage (d) Common-base output stage 1.10 The logical expression y A AB = + is equivalent to (a) y AB = (b) y AB = (c) y A B = + (d) y A B = + 1.11 A Darlington emitter-follower circuit is sometimes used in the output stage of a TTL gate in order to (a) increase its I OL (b) reduces its I OH (c) increases its speed of operation (d) reduce power dissipation 1.12 Commercially available ECL gears use two ground lines and one negative supply in order to (a) reduce power dissipation (b) increase fan-out (c) reduce loading effect (d) eliminate the effect of power line glitches or the biasing circuit V i V o Q 2 Q 1 R L i o GATE EC - 1999 1.13 The resolution of a 4-bit counting ADC is 0.5 volts. For an analog input of 6.6 volts, the digital output of the ADC will be (a) 1011 (b) 1101 (c) 1100 (d) 1110 1.14 For a second-order system with the closed-loop transfer function ( ) 2 9 4 9 T s s s = + + The settling time for 2-percent band, in seconds, is (a) 1.5 (b) 2.0 (c) 3.0 (d) 4.0 1.15 The gain margin (in dB) of a system having the loop transfer function ( ) ( ) ( ) 2 1 G s H s s s = + is (a) 0 (b) 3 (c) 6 (d) 8 1.16 The system mode described by the state equations 0 1 0 2 3 1 1 1 X x u y x ? ? ? ? = + ? ? ? ? - ? ? ? ? = ? ? ? ? is: (a) controllable and observable (b) controllable, but not observable (c) observable, but not controllable (d) neither controllable nor observable 1.17 The phase margin (in degrees) of a system having the loop transfer function ( ) ( ) ( ) 2 3 1 G s H s s s = + is (a) 45° (b) -30° (c) 60° (d) 30° 1.18 A signal x(t) has a Fourier transform X(?). If x(t) is a real and odd fucntion of t, then X(?) is (a) a real and even function of ? (b) a imaginary and odd function of ? (c) an imaginary and even function of ? (d) a real and odd function of ? Page 4 GATE EC - 1999 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 â€“ 1.25) of ONE mark each. For each of these sub-questions, four possible alternatives (A,B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answers in the boxes corresponding to the questions only on the FIRST sheet of the answer book. 1.1 Identify which of the following is NOT a true of the graph shown in Fig.P1.1 (a) begh (b) defg (c) adfg (d) aegh 1.2 The z-transform F(z) of the function ( ) nT f nT a = is (a) T z z a - (b) T z z a + (c) T z z a - - (d) T z z a - + 1.3 If ( ) ( ) ( ) , then f t F s f t T ? ? ? ? = - ? ? ? ? is equal to (a) ( ) sT e F s (b) ( ) sT e F s - (c) ( ) 1 sT F s e + (d) ( ) 1 sT F s e - - 1.4 A 2-port network is shown in Fig.P1.4. the parameter 21 h for this network can be given by (a) 1 2 - (b) 1 2 + (c) 3 2 - (d) 3 2 + 1.5 The early effect in a bipolar junction transistor is caused by (a) fast turn-on (b) fast turn-off (c) large collector-base reverse bias (d) large emitter-base forward bias 1 2 3 4 5 a b c d e f g h V 1 10µF + V 2 R R R I 1 I 2 - + - GATE EC - 1999 1.6 The first dominant pole encountered in the frequency response of a compensated op-amp is approximately at (a) 5 Hz (b) 10 kHz (c) 1 MHz (d) 100 MHz 1.7 Negative feedback in an amplifier (a) reduces gain (b) increases frequency and phase distortions (c) reduces bandwidth (d) increase noise 1.8 In the cascade amplifier shown in Fig.P1.8, if the common-emitter stage(Q 1 ) has a transconductance 1 , m g and the common base stage (Q 2 ) has a transconductance 2 , m g then the overall transconductance o i i g v ? ? = ? ? ? ? of the cascade amplifier is (a) 1 m g (b) 2 m g (c) 1 2 m g (d) 2 2 m g 1.9 Crossover distortion behaviour is characteristic of (a) Class A output stage (b) Class B output stage (c) Class AB output stage (d) Common-base output stage 1.10 The logical expression y A AB = + is equivalent to (a) y AB = (b) y AB = (c) y A B = + (d) y A B = + 1.11 A Darlington emitter-follower circuit is sometimes used in the output stage of a TTL gate in order to (a) increase its I OL (b) reduces its I OH (c) increases its speed of operation (d) reduce power dissipation 1.12 Commercially available ECL gears use two ground lines and one negative supply in order to (a) reduce power dissipation (b) increase fan-out (c) reduce loading effect (d) eliminate the effect of power line glitches or the biasing circuit V i V o Q 2 Q 1 R L i o GATE EC - 1999 1.13 The resolution of a 4-bit counting ADC is 0.5 volts. For an analog input of 6.6 volts, the digital output of the ADC will be (a) 1011 (b) 1101 (c) 1100 (d) 1110 1.14 For a second-order system with the closed-loop transfer function ( ) 2 9 4 9 T s s s = + + The settling time for 2-percent band, in seconds, is (a) 1.5 (b) 2.0 (c) 3.0 (d) 4.0 1.15 The gain margin (in dB) of a system having the loop transfer function ( ) ( ) ( ) 2 1 G s H s s s = + is (a) 0 (b) 3 (c) 6 (d) 8 1.16 The system mode described by the state equations 0 1 0 2 3 1 1 1 X x u y x ? ? ? ? = + ? ? ? ? - ? ? ? ? = ? ? ? ? is: (a) controllable and observable (b) controllable, but not observable (c) observable, but not controllable (d) neither controllable nor observable 1.17 The phase margin (in degrees) of a system having the loop transfer function ( ) ( ) ( ) 2 3 1 G s H s s s = + is (a) 45° (b) -30° (c) 60° (d) 30° 1.18 A signal x(t) has a Fourier transform X(?). If x(t) is a real and odd fucntion of t, then X(?) is (a) a real and even function of ? (b) a imaginary and odd function of ? (c) an imaginary and even function of ? (d) a real and odd function of ? GATE EC - 1999 1.19. The input to a channel is a bandpass signal. It is obtained by linearly modulating a sinusoidal carrier with a single-tone signal. The output of the channel due to this input is given by ( ) ( ) ( ) 6 6 1 cos 100 10 cos 10 1.56 100 y t t t - ? ? = - - ? ? ? ? The group delay ( ) g t and the phase delay ( ) p t in seconds, of the channel are (a) 6 10 , 1.56 g p t t - = = (b) 6 1.56, 10 g p t t - = = (c) 8 6 10 , 1.56 10 g p t t - = = × (d) 8 10 , 1.56 g p t t = = 1.20. A modulated signal is given by, ( ) ( ) ( ) ( ) ( ) 1 2 cos 2 sin 2 c c s t m t f t m t f t p p = + where the baseband signal ( ) ( ) 1 2 and m t m t have bandwidths of 10 kHz and 15 kHz, respectively. The bandwidth of the modulated signal, in kHz, is (a) 10 (b) 15 (c) 25 (d) 30 1.21. A modulated signal is given by ( ) ( ) ( ) cos , at c s t e t u t ? ? - ? ? = + ? ? ? where a,? c and ? ? are positive constants, and c ? ? ? . The complex envelope of s(t) is given by (a) ( ) ( ) ( ) exp exp c at j t u t ? ? ? ? - + ? ? ? (b) ( ) ( ) ( ) exp exp at j t u t ? - ? (c) ( ) exp . j t u t ? ? ? ? ? ? (d) ( ) exp c j t ? ? ? ? + ? ? ? 1.22. An electric field on a plane is described by its potential ( ) 1 2 20 V r r - - = + where r is the distance from the source. The field is due to (a) a monopole (b) a dipole (c) both a monopole and a dipole (d) a quadrupole 1.23. Assuming perfect conductors of a transmission line, pure TEM propagation is NOT possible in (a) coaxial cable (b) air-filled cylindrical wave guide (c) parallel twin-wire line in air (d) semi-infinite parallel plate wave guide 1.24. Indicate which one of the following will NOT exist in a rectangular resonant cavity. (a) 110 TE (b) 011 TE (c) 110 TM (d) 111 TM Page 5 GATE EC - 1999 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 â€“ 1.25) of ONE mark each. For each of these sub-questions, four possible alternatives (A,B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answers in the boxes corresponding to the questions only on the FIRST sheet of the answer book. 1.1 Identify which of the following is NOT a true of the graph shown in Fig.P1.1 (a) begh (b) defg (c) adfg (d) aegh 1.2 The z-transform F(z) of the function ( ) nT f nT a = is (a) T z z a - (b) T z z a + (c) T z z a - - (d) T z z a - + 1.3 If ( ) ( ) ( ) , then f t F s f t T ? ? ? ? = - ? ? ? ? is equal to (a) ( ) sT e F s (b) ( ) sT e F s - (c) ( ) 1 sT F s e + (d) ( ) 1 sT F s e - - 1.4 A 2-port network is shown in Fig.P1.4. the parameter 21 h for this network can be given by (a) 1 2 - (b) 1 2 + (c) 3 2 - (d) 3 2 + 1.5 The early effect in a bipolar junction transistor is caused by (a) fast turn-on (b) fast turn-off (c) large collector-base reverse bias (d) large emitter-base forward bias 1 2 3 4 5 a b c d e f g h V 1 10µF + V 2 R R R I 1 I 2 - + - GATE EC - 1999 1.6 The first dominant pole encountered in the frequency response of a compensated op-amp is approximately at (a) 5 Hz (b) 10 kHz (c) 1 MHz (d) 100 MHz 1.7 Negative feedback in an amplifier (a) reduces gain (b) increases frequency and phase distortions (c) reduces bandwidth (d) increase noise 1.8 In the cascade amplifier shown in Fig.P1.8, if the common-emitter stage(Q 1 ) has a transconductance 1 , m g and the common base stage (Q 2 ) has a transconductance 2 , m g then the overall transconductance o i i g v ? ? = ? ? ? ? of the cascade amplifier is (a) 1 m g (b) 2 m g (c) 1 2 m g (d) 2 2 m g 1.9 Crossover distortion behaviour is characteristic of (a) Class A output stage (b) Class B output stage (c) Class AB output stage (d) Common-base output stage 1.10 The logical expression y A AB = + is equivalent to (a) y AB = (b) y AB = (c) y A B = + (d) y A B = + 1.11 A Darlington emitter-follower circuit is sometimes used in the output stage of a TTL gate in order to (a) increase its I OL (b) reduces its I OH (c) increases its speed of operation (d) reduce power dissipation 1.12 Commercially available ECL gears use two ground lines and one negative supply in order to (a) reduce power dissipation (b) increase fan-out (c) reduce loading effect (d) eliminate the effect of power line glitches or the biasing circuit V i V o Q 2 Q 1 R L i o GATE EC - 1999 1.13 The resolution of a 4-bit counting ADC is 0.5 volts. For an analog input of 6.6 volts, the digital output of the ADC will be (a) 1011 (b) 1101 (c) 1100 (d) 1110 1.14 For a second-order system with the closed-loop transfer function ( ) 2 9 4 9 T s s s = + + The settling time for 2-percent band, in seconds, is (a) 1.5 (b) 2.0 (c) 3.0 (d) 4.0 1.15 The gain margin (in dB) of a system having the loop transfer function ( ) ( ) ( ) 2 1 G s H s s s = + is (a) 0 (b) 3 (c) 6 (d) 8 1.16 The system mode described by the state equations 0 1 0 2 3 1 1 1 X x u y x ? ? ? ? = + ? ? ? ? - ? ? ? ? = ? ? ? ? is: (a) controllable and observable (b) controllable, but not observable (c) observable, but not controllable (d) neither controllable nor observable 1.17 The phase margin (in degrees) of a system having the loop transfer function ( ) ( ) ( ) 2 3 1 G s H s s s = + is (a) 45° (b) -30° (c) 60° (d) 30° 1.18 A signal x(t) has a Fourier transform X(?). If x(t) is a real and odd fucntion of t, then X(?) is (a) a real and even function of ? (b) a imaginary and odd function of ? (c) an imaginary and even function of ? (d) a real and odd function of ? GATE EC - 1999 1.19. The input to a channel is a bandpass signal. It is obtained by linearly modulating a sinusoidal carrier with a single-tone signal. The output of the channel due to this input is given by ( ) ( ) ( ) 6 6 1 cos 100 10 cos 10 1.56 100 y t t t - ? ? = - - ? ? ? ? The group delay ( ) g t and the phase delay ( ) p t in seconds, of the channel are (a) 6 10 , 1.56 g p t t - = = (b) 6 1.56, 10 g p t t - = = (c) 8 6 10 , 1.56 10 g p t t - = = × (d) 8 10 , 1.56 g p t t = = 1.20. A modulated signal is given by, ( ) ( ) ( ) ( ) ( ) 1 2 cos 2 sin 2 c c s t m t f t m t f t p p = + where the baseband signal ( ) ( ) 1 2 and m t m t have bandwidths of 10 kHz and 15 kHz, respectively. The bandwidth of the modulated signal, in kHz, is (a) 10 (b) 15 (c) 25 (d) 30 1.21. A modulated signal is given by ( ) ( ) ( ) cos , at c s t e t u t ? ? - ? ? = + ? ? ? where a,? c and ? ? are positive constants, and c ? ? ? . The complex envelope of s(t) is given by (a) ( ) ( ) ( ) exp exp c at j t u t ? ? ? ? - + ? ? ? (b) ( ) ( ) ( ) exp exp at j t u t ? - ? (c) ( ) exp . j t u t ? ? ? ? ? ? (d) ( ) exp c j t ? ? ? ? + ? ? ? 1.22. An electric field on a plane is described by its potential ( ) 1 2 20 V r r - - = + where r is the distance from the source. The field is due to (a) a monopole (b) a dipole (c) both a monopole and a dipole (d) a quadrupole 1.23. Assuming perfect conductors of a transmission line, pure TEM propagation is NOT possible in (a) coaxial cable (b) air-filled cylindrical wave guide (c) parallel twin-wire line in air (d) semi-infinite parallel plate wave guide 1.24. Indicate which one of the following will NOT exist in a rectangular resonant cavity. (a) 110 TE (b) 011 TE (c) 110 TM (d) 111 TM GATE EC - 1999 ? a b c 5O 30O 15O a b c R 1 R 2 R 3 1.25 Identify which one of the following will NOT satisfy the wave equation. (a) ( ) 3 50 j t z e ? - (b) ( ) sin 10 5 z t ? ? ? + ? ? (c) ( ) 2 cos 5 y t + (d) ( ) ( ) sin cos x t 2. This question consists of TWENTY-FIVE sub-questions (2.1 â€“ 2.25) of ONE mark each. For each of these sub-questions, four possible alternatives (A, B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answers in the boxes corresponding to the questions only on the SECOND sheet of the answer book. 2.1 The Fourier series representation of an impulses train denoted by ( ) ( ) 0 n s t d t nT 8 =-8 = - ? is given by (a) 0 0 1 2 exp n j nt T T p 8 =-8 - ? (b) 0 0 1 exp n j nt T T p 8 =-8 - ? (c) 0 0 1 exp n j nt T T p 8 =-8 ? (d) 0 0 1 2 exp n j nt T T p 8 =-8 ? 2.2. The Thevenin equivalent voltage TH V appearing between the terminals A and B of the network shown in Fig.P2.2 is given by (a) j16(3-j4) (b) j16(3+j4) (c) 16(3+j4) (d) 16(3-j4) 2.3. The value of R (in ohms) required for maximum power transfer in the network shown in Fig.P2.3 is (a) 2 (b) 4 (c) 8 (d) 10 2.4. A Delta-connected network with its Wye-equivalent is shown in Fig.P2.4. The resistance R 1 , R 2 and R 3 (in ohms) are respectively 100?0°V 3O V TH j2 A ~ -j6 j4 B + - 3A 5O 4O 25V + - R 20ORead More

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