Page 1 GATE EC - 2002 V D 1mA + - SECTION â€“ A (75 marks) 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 answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 1.1 The dependent current source shown in Figure 1.1 (a) delivers 80 W (b) absorbs 80 W (c) delivers 40 W (d) absorbs 40 W 1.2 In figure 1.2, the switch was closed for a long time before opening at t = 0. the voltage Vx at t = 0 + is (a) 25 V (b) 50 V (c) -50 V (d) 0 V 1.3 Convolution of x(t + 5) with impulse function d(t â€“ 7) is equal to (a) x(t - 12) (b) x(t + 12) (c) x(t - 2) (d) x(t + 2) 1.4 Which of the following cannot be the Fourier series expansion of a periodic signal? (a) x(t) = 2cos t + 3 cos 3t (b) x(t) = 2cos pt + 7 cos t (c) x(t) = cos t + 0.5 (d) x(t) = 2cos 1.5pt + sin 3.5 pt 1.5 In Figure 1.5, a silicon is carrying a constant current of 1 mA. When the temperature of the diode is 20°C, V D is found to be 700 mV. If the temperature rises to 40°C, V D becomes approximately equal to (a) 740 mV (b) 660 mV (c) 680 mV (d) 700 mV 5O 1 5 V A V 1=20V I 5O + - 2.5A 5H 20O 20O t=0 V x + - Page 2 GATE EC - 2002 V D 1mA + - SECTION â€“ A (75 marks) 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 answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 1.1 The dependent current source shown in Figure 1.1 (a) delivers 80 W (b) absorbs 80 W (c) delivers 40 W (d) absorbs 40 W 1.2 In figure 1.2, the switch was closed for a long time before opening at t = 0. the voltage Vx at t = 0 + is (a) 25 V (b) 50 V (c) -50 V (d) 0 V 1.3 Convolution of x(t + 5) with impulse function d(t â€“ 7) is equal to (a) x(t - 12) (b) x(t + 12) (c) x(t - 2) (d) x(t + 2) 1.4 Which of the following cannot be the Fourier series expansion of a periodic signal? (a) x(t) = 2cos t + 3 cos 3t (b) x(t) = 2cos pt + 7 cos t (c) x(t) = cos t + 0.5 (d) x(t) = 2cos 1.5pt + sin 3.5 pt 1.5 In Figure 1.5, a silicon is carrying a constant current of 1 mA. When the temperature of the diode is 20°C, V D is found to be 700 mV. If the temperature rises to 40°C, V D becomes approximately equal to (a) 740 mV (b) 660 mV (c) 680 mV (d) 700 mV 5O 1 5 V A V 1=20V I 5O + - 2.5A 5H 20O 20O t=0 V x + - GATE EC - 2002 1.6 In a negative feedback amplifier using voltage-series (i.e. voltage-sampling series mixing) feedback. (R i and R o denote the input and output resistance respectively) (a) R i decreases and R o decreases (b) R i decreases and R o increases (c) R i increases and R o decreases (d) R i increases and R o increases 1.7 A 741-type op-amp has a gain-bandwidth product of 1 MHz. A non-inverting amplifier using this op-amp and having a voltage gain of 20 dB will exhibit a 3-dB bandwidth of (a) 50 KHz (b) 100 KHz (c) 1000 17 KHz (d) 1000 7.07 1.8 Three identical RC-coupled transistor amplifiers are cascaded. If each of the amplifiers has a frequency response as shown in Figure 1.8, the overall frequency response is as given in (a) (b) (c) (d) 1.9 4-bit 2â€™s complement representation of a decimal number is 1000. The number is (a) +8 (b) 0 (c) -7 (d) -8 f 20Hz 1KHz -3 0 v A dB f 40Hz 0.5KHz -3 0 v A dB 2 40Hz 1KHz -3 0 v A dB f 40Hz 2KHz -3 f v A dB 0 10Hz 0.5KHz -3 f v A dB 0 Page 3 GATE EC - 2002 V D 1mA + - SECTION â€“ A (75 marks) 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 answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 1.1 The dependent current source shown in Figure 1.1 (a) delivers 80 W (b) absorbs 80 W (c) delivers 40 W (d) absorbs 40 W 1.2 In figure 1.2, the switch was closed for a long time before opening at t = 0. the voltage Vx at t = 0 + is (a) 25 V (b) 50 V (c) -50 V (d) 0 V 1.3 Convolution of x(t + 5) with impulse function d(t â€“ 7) is equal to (a) x(t - 12) (b) x(t + 12) (c) x(t - 2) (d) x(t + 2) 1.4 Which of the following cannot be the Fourier series expansion of a periodic signal? (a) x(t) = 2cos t + 3 cos 3t (b) x(t) = 2cos pt + 7 cos t (c) x(t) = cos t + 0.5 (d) x(t) = 2cos 1.5pt + sin 3.5 pt 1.5 In Figure 1.5, a silicon is carrying a constant current of 1 mA. When the temperature of the diode is 20°C, V D is found to be 700 mV. If the temperature rises to 40°C, V D becomes approximately equal to (a) 740 mV (b) 660 mV (c) 680 mV (d) 700 mV 5O 1 5 V A V 1=20V I 5O + - 2.5A 5H 20O 20O t=0 V x + - GATE EC - 2002 1.6 In a negative feedback amplifier using voltage-series (i.e. voltage-sampling series mixing) feedback. (R i and R o denote the input and output resistance respectively) (a) R i decreases and R o decreases (b) R i decreases and R o increases (c) R i increases and R o decreases (d) R i increases and R o increases 1.7 A 741-type op-amp has a gain-bandwidth product of 1 MHz. A non-inverting amplifier using this op-amp and having a voltage gain of 20 dB will exhibit a 3-dB bandwidth of (a) 50 KHz (b) 100 KHz (c) 1000 17 KHz (d) 1000 7.07 1.8 Three identical RC-coupled transistor amplifiers are cascaded. If each of the amplifiers has a frequency response as shown in Figure 1.8, the overall frequency response is as given in (a) (b) (c) (d) 1.9 4-bit 2â€™s complement representation of a decimal number is 1000. The number is (a) +8 (b) 0 (c) -7 (d) -8 f 20Hz 1KHz -3 0 v A dB f 40Hz 0.5KHz -3 0 v A dB 2 40Hz 1KHz -3 0 v A dB f 40Hz 2KHz -3 f v A dB 0 10Hz 0.5KHz -3 f v A dB 0 GATE EC - 2002 1.10 If the input to the digital circuit (Figure 1.10) consisting of a cascade of 20 XOR- gates is X, then the output Y is equal to (a) 0 (b) 1 (c) X (d) X 1.11 The number of comparators required in a 3-bit comparator type ADC is (a) 2 (b) 3 (c) 7 (d) 8 1.12 If the transistor in Figure 1.12 is in saturation, then (a) I C is always equal to ß dc I B (b) I C is always equal to -ß dc I B (c) I C is greater than or equal to ß dc I B (d) I C is less than or equal to ß dc I B 1.13 Consider a system with the transfer function ( ) 2 6 . 6 s G s ks s + = + + Its damping ratio will be 0.5 when the value of k is (a) 2 6 (b) 3 (c) 1 6 (d) 6 1.14 Which of the following points is NOT on the root locus of a system with the open loop transfer function ( ) ( ) ( )( ) 1 3 k G s H s s s s = + + (a) s = 3 j - (b) s= - 1.5 (c) s= -3 (d) s = -8 1 X Y C ß dc denotes the dc current gain E I C I B Page 4 GATE EC - 2002 V D 1mA + - SECTION â€“ A (75 marks) 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 answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 1.1 The dependent current source shown in Figure 1.1 (a) delivers 80 W (b) absorbs 80 W (c) delivers 40 W (d) absorbs 40 W 1.2 In figure 1.2, the switch was closed for a long time before opening at t = 0. the voltage Vx at t = 0 + is (a) 25 V (b) 50 V (c) -50 V (d) 0 V 1.3 Convolution of x(t + 5) with impulse function d(t â€“ 7) is equal to (a) x(t - 12) (b) x(t + 12) (c) x(t - 2) (d) x(t + 2) 1.4 Which of the following cannot be the Fourier series expansion of a periodic signal? (a) x(t) = 2cos t + 3 cos 3t (b) x(t) = 2cos pt + 7 cos t (c) x(t) = cos t + 0.5 (d) x(t) = 2cos 1.5pt + sin 3.5 pt 1.5 In Figure 1.5, a silicon is carrying a constant current of 1 mA. When the temperature of the diode is 20°C, V D is found to be 700 mV. If the temperature rises to 40°C, V D becomes approximately equal to (a) 740 mV (b) 660 mV (c) 680 mV (d) 700 mV 5O 1 5 V A V 1=20V I 5O + - 2.5A 5H 20O 20O t=0 V x + - GATE EC - 2002 1.6 In a negative feedback amplifier using voltage-series (i.e. voltage-sampling series mixing) feedback. (R i and R o denote the input and output resistance respectively) (a) R i decreases and R o decreases (b) R i decreases and R o increases (c) R i increases and R o decreases (d) R i increases and R o increases 1.7 A 741-type op-amp has a gain-bandwidth product of 1 MHz. A non-inverting amplifier using this op-amp and having a voltage gain of 20 dB will exhibit a 3-dB bandwidth of (a) 50 KHz (b) 100 KHz (c) 1000 17 KHz (d) 1000 7.07 1.8 Three identical RC-coupled transistor amplifiers are cascaded. If each of the amplifiers has a frequency response as shown in Figure 1.8, the overall frequency response is as given in (a) (b) (c) (d) 1.9 4-bit 2â€™s complement representation of a decimal number is 1000. The number is (a) +8 (b) 0 (c) -7 (d) -8 f 20Hz 1KHz -3 0 v A dB f 40Hz 0.5KHz -3 0 v A dB 2 40Hz 1KHz -3 0 v A dB f 40Hz 2KHz -3 f v A dB 0 10Hz 0.5KHz -3 f v A dB 0 GATE EC - 2002 1.10 If the input to the digital circuit (Figure 1.10) consisting of a cascade of 20 XOR- gates is X, then the output Y is equal to (a) 0 (b) 1 (c) X (d) X 1.11 The number of comparators required in a 3-bit comparator type ADC is (a) 2 (b) 3 (c) 7 (d) 8 1.12 If the transistor in Figure 1.12 is in saturation, then (a) I C is always equal to ß dc I B (b) I C is always equal to -ß dc I B (c) I C is greater than or equal to ß dc I B (d) I C is less than or equal to ß dc I B 1.13 Consider a system with the transfer function ( ) 2 6 . 6 s G s ks s + = + + Its damping ratio will be 0.5 when the value of k is (a) 2 6 (b) 3 (c) 1 6 (d) 6 1.14 Which of the following points is NOT on the root locus of a system with the open loop transfer function ( ) ( ) ( )( ) 1 3 k G s H s s s s = + + (a) s = 3 j - (b) s= - 1.5 (c) s= -3 (d) s = -8 1 X Y C ß dc denotes the dc current gain E I C I B GATE EC - 2002 1.15 The phase margin of a system with the open-loop transfer function ( ) ( ) ( ) ( )( ) 1 1 2 s G s H s s s - = + + is (a) 0° (b) 63.4° (c) 90° (d) 8 1.16 The transfer function ( ) ( ) Y s U s of a system described by the state equations x(t) = -2x(t) + 2u(t) and y(t) = 0.5x(t) is (a) ( ) 0.5 2 s - (b) ( ) 1 2 s - (c) ( ) 0.5 2 s + (d) ( ) 1 2 s + 1.17 The Fourier transform ( ) { } 1 F e u t - is equal to 1 . 1 2 j f p + Therefore, 1 1 2 F j t p ? ? ? ? + ? ? is (a) ( ) f e u f (b) ( ) f e u f - (c) ( ) f e u f - (d) ( ) f e u f - - 1.18 A linear phase channel with phase delay T P and group delay T g must have (a) T P = T g =constant (b) T P ?f and T g ?f (c) T P = constant and T g ?f (d) T P ?f and T g =constant 1.19. A 1 MHz sinusoidal carrier is amplitude modulated by a symmetrical square wave of period 100µsec. Which of the following frequencies will NOT be present in the modulated signal? (a) 990 KHz (b) 1010 KHz (c) 1020 KHz (d) 1030 KHz 1.20. Consider a sampled signal ( ) ( ) ( ) 6 5 10 s n y t x t t nT d +8 - =-8 = × - ? where x(t) =10 cos(8p×10 3 )t and T s =100µsec. When y(t) is passed through an ideal low-pass filter with a cutoff frequency of 5KHz, the output of the filter is (a) ( ) 6 3 5 10 cos 8 10 t p - × × (b) ( ) 5 3 5 10 cos 8 10 t p - × × (c) ( ) 1 3 5 10 cos 8 10 t p - × × (d) ( ) 3 10cos 8 10 t p × 1.21. For a bit-rate of 8 Kbps, the best possible values of the transmitted frequencies in a coherent binary FSK system are (a) 16 KHz and 20 KHz (b) 20 KHz and 32 KHz (c) 20 KHz and 40 KHz (d) 32 KHz and 40 KHz 1.22. The line-of-sight communication requires the transmit and receive antenna to face each other. If the transmit antenna is vertically polarized, for best reception the receive antenna should be (a) horizontally polarized (b) vertically polarized Page 5 GATE EC - 2002 V D 1mA + - SECTION â€“ A (75 marks) 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 answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 1.1 The dependent current source shown in Figure 1.1 (a) delivers 80 W (b) absorbs 80 W (c) delivers 40 W (d) absorbs 40 W 1.2 In figure 1.2, the switch was closed for a long time before opening at t = 0. the voltage Vx at t = 0 + is (a) 25 V (b) 50 V (c) -50 V (d) 0 V 1.3 Convolution of x(t + 5) with impulse function d(t â€“ 7) is equal to (a) x(t - 12) (b) x(t + 12) (c) x(t - 2) (d) x(t + 2) 1.4 Which of the following cannot be the Fourier series expansion of a periodic signal? (a) x(t) = 2cos t + 3 cos 3t (b) x(t) = 2cos pt + 7 cos t (c) x(t) = cos t + 0.5 (d) x(t) = 2cos 1.5pt + sin 3.5 pt 1.5 In Figure 1.5, a silicon is carrying a constant current of 1 mA. When the temperature of the diode is 20°C, V D is found to be 700 mV. If the temperature rises to 40°C, V D becomes approximately equal to (a) 740 mV (b) 660 mV (c) 680 mV (d) 700 mV 5O 1 5 V A V 1=20V I 5O + - 2.5A 5H 20O 20O t=0 V x + - GATE EC - 2002 1.6 In a negative feedback amplifier using voltage-series (i.e. voltage-sampling series mixing) feedback. (R i and R o denote the input and output resistance respectively) (a) R i decreases and R o decreases (b) R i decreases and R o increases (c) R i increases and R o decreases (d) R i increases and R o increases 1.7 A 741-type op-amp has a gain-bandwidth product of 1 MHz. A non-inverting amplifier using this op-amp and having a voltage gain of 20 dB will exhibit a 3-dB bandwidth of (a) 50 KHz (b) 100 KHz (c) 1000 17 KHz (d) 1000 7.07 1.8 Three identical RC-coupled transistor amplifiers are cascaded. If each of the amplifiers has a frequency response as shown in Figure 1.8, the overall frequency response is as given in (a) (b) (c) (d) 1.9 4-bit 2â€™s complement representation of a decimal number is 1000. The number is (a) +8 (b) 0 (c) -7 (d) -8 f 20Hz 1KHz -3 0 v A dB f 40Hz 0.5KHz -3 0 v A dB 2 40Hz 1KHz -3 0 v A dB f 40Hz 2KHz -3 f v A dB 0 10Hz 0.5KHz -3 f v A dB 0 GATE EC - 2002 1.10 If the input to the digital circuit (Figure 1.10) consisting of a cascade of 20 XOR- gates is X, then the output Y is equal to (a) 0 (b) 1 (c) X (d) X 1.11 The number of comparators required in a 3-bit comparator type ADC is (a) 2 (b) 3 (c) 7 (d) 8 1.12 If the transistor in Figure 1.12 is in saturation, then (a) I C is always equal to ß dc I B (b) I C is always equal to -ß dc I B (c) I C is greater than or equal to ß dc I B (d) I C is less than or equal to ß dc I B 1.13 Consider a system with the transfer function ( ) 2 6 . 6 s G s ks s + = + + Its damping ratio will be 0.5 when the value of k is (a) 2 6 (b) 3 (c) 1 6 (d) 6 1.14 Which of the following points is NOT on the root locus of a system with the open loop transfer function ( ) ( ) ( )( ) 1 3 k G s H s s s s = + + (a) s = 3 j - (b) s= - 1.5 (c) s= -3 (d) s = -8 1 X Y C ß dc denotes the dc current gain E I C I B GATE EC - 2002 1.15 The phase margin of a system with the open-loop transfer function ( ) ( ) ( ) ( )( ) 1 1 2 s G s H s s s - = + + is (a) 0° (b) 63.4° (c) 90° (d) 8 1.16 The transfer function ( ) ( ) Y s U s of a system described by the state equations x(t) = -2x(t) + 2u(t) and y(t) = 0.5x(t) is (a) ( ) 0.5 2 s - (b) ( ) 1 2 s - (c) ( ) 0.5 2 s + (d) ( ) 1 2 s + 1.17 The Fourier transform ( ) { } 1 F e u t - is equal to 1 . 1 2 j f p + Therefore, 1 1 2 F j t p ? ? ? ? + ? ? is (a) ( ) f e u f (b) ( ) f e u f - (c) ( ) f e u f - (d) ( ) f e u f - - 1.18 A linear phase channel with phase delay T P and group delay T g must have (a) T P = T g =constant (b) T P ?f and T g ?f (c) T P = constant and T g ?f (d) T P ?f and T g =constant 1.19. A 1 MHz sinusoidal carrier is amplitude modulated by a symmetrical square wave of period 100µsec. Which of the following frequencies will NOT be present in the modulated signal? (a) 990 KHz (b) 1010 KHz (c) 1020 KHz (d) 1030 KHz 1.20. Consider a sampled signal ( ) ( ) ( ) 6 5 10 s n y t x t t nT d +8 - =-8 = × - ? where x(t) =10 cos(8p×10 3 )t and T s =100µsec. When y(t) is passed through an ideal low-pass filter with a cutoff frequency of 5KHz, the output of the filter is (a) ( ) 6 3 5 10 cos 8 10 t p - × × (b) ( ) 5 3 5 10 cos 8 10 t p - × × (c) ( ) 1 3 5 10 cos 8 10 t p - × × (d) ( ) 3 10cos 8 10 t p × 1.21. For a bit-rate of 8 Kbps, the best possible values of the transmitted frequencies in a coherent binary FSK system are (a) 16 KHz and 20 KHz (b) 20 KHz and 32 KHz (c) 20 KHz and 40 KHz (d) 32 KHz and 40 KHz 1.22. The line-of-sight communication requires the transmit and receive antenna to face each other. If the transmit antenna is vertically polarized, for best reception the receive antenna should be (a) horizontally polarized (b) vertically polarized GATE EC - 2002 (c) at 45° with respect to horizontal polarization (d) at 45° with respect to vertical polarization 1.23. The VSWR can have any value between (a) 0 and 1 (b) -1 and +1 (c) 0 and 8 (d) 1 and 8 1.24. In an impedance Smith chart, a clockwise movement along a constant resistance circle gives rise to (a) a decrease in the value of reactance (b) an increase in the value of reactance (c) no change in the reactance value (d) no change in the impedance value 1.25 The phase velocity for the TE 10 -mode in an air-filled rectangular waveguide is (c is the velocity of plane waves in free space) (a) less than c (b) equal to c (c) greater than c (d) none of the above 2. This question consists of TWENTY-FIVE sub-questions (2.1 â€“ 2.25) of TWO marks 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 answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 2.1 In the network of Figure 2.1, the maximum power is delivered to R L if its value is (a) 16O (b) 40 3 O (c) 60O (d) 20O I 1 40O 50V R L 20O 0.5I 1Read More

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