Page 1 GATE EC - 1992 Time: 3 hours Maximum Marks: 200 Part A: 80 Marks Part B: 120 Marks 1. This paper consists of two parts: “Part A” and “Part B”. 2. Part A contains 40 questions, each carrying 2 marks. 3. Part B contains 15 questions, each carrying 8 marks. 4. Read the instructions given at the beginning of each part carefully. 5. Attempt ALL questions. 6. There is no negative marking. PART – A 1.1 Relative to a given fixed tree of a network, (a) Link currents form an independent set (b) Branch voltage from an independent set (c) Link currents from an independent set (d) Branch voltage from an independent set 1.2 For a 2-port network to be reciprocal (a) 11 22 z z = (b) 21 12 y y = (c) 21 12 h h = - (d) 0 AD BC - = 1.3 For the series R-L circuit of figure(a), the partial fissure diagram at a certain frequency is shown in figure (b).The operating frequency of the circuit is: (a) equal to the resonance frequency (b) less than the resonance frequency (c) greater than resonance frequency (d) not zero 1.4 For the compensated attenuator of figure, the impulse response under the condition 1 1 2 2 R C R C = is: (a) ( ) 1 1 1 2 1 2 1 R C R e u t R R ? ? - ? ? + ? ? ? ? (b) ( ) 2 1 2 R t R R d + (c) ( ) 2 1 2 R u t R R + (d) ( ) 1 1 1 2 1 2 1 . R C R e u t R R - + + - V + - + - R V L V C V + - (a) R V V C V (b) + - + - C 2 C 1 V 1(t) V 2(t) R 1 R 2(t) C Page 2 GATE EC - 1992 Time: 3 hours Maximum Marks: 200 Part A: 80 Marks Part B: 120 Marks 1. This paper consists of two parts: “Part A” and “Part B”. 2. Part A contains 40 questions, each carrying 2 marks. 3. Part B contains 15 questions, each carrying 8 marks. 4. Read the instructions given at the beginning of each part carefully. 5. Attempt ALL questions. 6. There is no negative marking. PART – A 1.1 Relative to a given fixed tree of a network, (a) Link currents form an independent set (b) Branch voltage from an independent set (c) Link currents from an independent set (d) Branch voltage from an independent set 1.2 For a 2-port network to be reciprocal (a) 11 22 z z = (b) 21 12 y y = (c) 21 12 h h = - (d) 0 AD BC - = 1.3 For the series R-L circuit of figure(a), the partial fissure diagram at a certain frequency is shown in figure (b).The operating frequency of the circuit is: (a) equal to the resonance frequency (b) less than the resonance frequency (c) greater than resonance frequency (d) not zero 1.4 For the compensated attenuator of figure, the impulse response under the condition 1 1 2 2 R C R C = is: (a) ( ) 1 1 1 2 1 2 1 R C R e u t R R ? ? - ? ? + ? ? ? ? (b) ( ) 2 1 2 R t R R d + (c) ( ) 2 1 2 R u t R R + (d) ( ) 1 1 1 2 1 2 1 . R C R e u t R R - + + - V + - + - R V L V C V + - (a) R V V C V (b) + - + - C 2 C 1 V 1(t) V 2(t) R 1 R 2(t) C GATE EC - 1992 1.5 Of the four networks, 1 2 3 4 , , and N N N N of figure, the networks having identical driving point functions are (a) 1 1 and N N (b) 2 4 and N N (c) 1 3 and N N (d) 1 4 and N N 1.6 A linear time invariant system is described by the state variable model 1 1 1 2 2 2 1 0 0 1 2 0 2 1 x x x u x x x - ? ? ? ? ? ? ? ? ? ? = + = ? ? ? ? ? ? ? ? ? ? ? ? ? ? - ? ? ? ? ? ? ? ? ? ? (a) The system is completely controllable (b) The system is not completely controllable (c) The system is completely observable (d) The system is not completely observable 1.7 A process with open-loop model ( ) 4 1 sT ke G s s t - = + is controlled by a PID controller. For this process (a) the integral mode improves transient performance (b) the integral mode improves steady state performance (c) the derivative mode improves transient performance (d) the derivative mode improves steady state performance 1.8 A linear discrete time system has the characteristic equation, 3 0.81 0. z z - = The system (a) is stable (b) is marginally stable (c) in unstable (d) stability cannot be assessed from the given information 2 1 2 1 1 N 1 2 1 1 N 2 2 2 1 1 N 3 1 1 1 1 N 4 2 Page 3 GATE EC - 1992 Time: 3 hours Maximum Marks: 200 Part A: 80 Marks Part B: 120 Marks 1. This paper consists of two parts: “Part A” and “Part B”. 2. Part A contains 40 questions, each carrying 2 marks. 3. Part B contains 15 questions, each carrying 8 marks. 4. Read the instructions given at the beginning of each part carefully. 5. Attempt ALL questions. 6. There is no negative marking. PART – A 1.1 Relative to a given fixed tree of a network, (a) Link currents form an independent set (b) Branch voltage from an independent set (c) Link currents from an independent set (d) Branch voltage from an independent set 1.2 For a 2-port network to be reciprocal (a) 11 22 z z = (b) 21 12 y y = (c) 21 12 h h = - (d) 0 AD BC - = 1.3 For the series R-L circuit of figure(a), the partial fissure diagram at a certain frequency is shown in figure (b).The operating frequency of the circuit is: (a) equal to the resonance frequency (b) less than the resonance frequency (c) greater than resonance frequency (d) not zero 1.4 For the compensated attenuator of figure, the impulse response under the condition 1 1 2 2 R C R C = is: (a) ( ) 1 1 1 2 1 2 1 R C R e u t R R ? ? - ? ? + ? ? ? ? (b) ( ) 2 1 2 R t R R d + (c) ( ) 2 1 2 R u t R R + (d) ( ) 1 1 1 2 1 2 1 . R C R e u t R R - + + - V + - + - R V L V C V + - (a) R V V C V (b) + - + - C 2 C 1 V 1(t) V 2(t) R 1 R 2(t) C GATE EC - 1992 1.5 Of the four networks, 1 2 3 4 , , and N N N N of figure, the networks having identical driving point functions are (a) 1 1 and N N (b) 2 4 and N N (c) 1 3 and N N (d) 1 4 and N N 1.6 A linear time invariant system is described by the state variable model 1 1 1 2 2 2 1 0 0 1 2 0 2 1 x x x u x x x - ? ? ? ? ? ? ? ? ? ? = + = ? ? ? ? ? ? ? ? ? ? ? ? ? ? - ? ? ? ? ? ? ? ? ? ? (a) The system is completely controllable (b) The system is not completely controllable (c) The system is completely observable (d) The system is not completely observable 1.7 A process with open-loop model ( ) 4 1 sT ke G s s t - = + is controlled by a PID controller. For this process (a) the integral mode improves transient performance (b) the integral mode improves steady state performance (c) the derivative mode improves transient performance (d) the derivative mode improves steady state performance 1.8 A linear discrete time system has the characteristic equation, 3 0.81 0. z z - = The system (a) is stable (b) is marginally stable (c) in unstable (d) stability cannot be assessed from the given information 2 1 2 1 1 N 1 2 1 1 N 2 2 2 1 1 N 3 1 1 1 1 N 4 2 GATE EC - 1992 1.9 Bode plot of a stable system is shown in figure. The transfer function of the system is _______. 1.10 Given a unity feedback system with open loop transfer function, ( ) ( )( ) . 1 2 K G s s s s = + + The root locus plot of the system is of the form. 1.11 A semiconductor is irradiated with light such that carriers are uniformly generated throughout its volume. The semiconductor is n-type with 19 10 D N = per 3 . cm If the excess electron concentration in the steady state id 15 10 n ? = per 3 cm and if 10 sec p t µ = [minority carrier life time] the generation rate due to irradiation (a) is 20 3 10 pair/cm / e h s - (b) is 24 3 10 pair/cm / e h s - (c) is 10 3 10 pair/cm / e h s - (d) cannot be determined as the given data is insufficient 1.12 A P – N junction in series with a 100 ohms resistor, is forward biased so that a current of 100 mA flows. If the voltage across this combination is instantaneously reversed to 10 V at t = 0, the reverse current that flows through the diode at t = 0 is approximately given by (a) 0 mA (b) 100 mA (c) 200 mA (d) 50 mA dB 20 20 dB/Decade log ? × × × s j? × × × s j? × × × s j? × × × j? s Page 4 GATE EC - 1992 Time: 3 hours Maximum Marks: 200 Part A: 80 Marks Part B: 120 Marks 1. This paper consists of two parts: “Part A” and “Part B”. 2. Part A contains 40 questions, each carrying 2 marks. 3. Part B contains 15 questions, each carrying 8 marks. 4. Read the instructions given at the beginning of each part carefully. 5. Attempt ALL questions. 6. There is no negative marking. PART – A 1.1 Relative to a given fixed tree of a network, (a) Link currents form an independent set (b) Branch voltage from an independent set (c) Link currents from an independent set (d) Branch voltage from an independent set 1.2 For a 2-port network to be reciprocal (a) 11 22 z z = (b) 21 12 y y = (c) 21 12 h h = - (d) 0 AD BC - = 1.3 For the series R-L circuit of figure(a), the partial fissure diagram at a certain frequency is shown in figure (b).The operating frequency of the circuit is: (a) equal to the resonance frequency (b) less than the resonance frequency (c) greater than resonance frequency (d) not zero 1.4 For the compensated attenuator of figure, the impulse response under the condition 1 1 2 2 R C R C = is: (a) ( ) 1 1 1 2 1 2 1 R C R e u t R R ? ? - ? ? + ? ? ? ? (b) ( ) 2 1 2 R t R R d + (c) ( ) 2 1 2 R u t R R + (d) ( ) 1 1 1 2 1 2 1 . R C R e u t R R - + + - V + - + - R V L V C V + - (a) R V V C V (b) + - + - C 2 C 1 V 1(t) V 2(t) R 1 R 2(t) C GATE EC - 1992 1.5 Of the four networks, 1 2 3 4 , , and N N N N of figure, the networks having identical driving point functions are (a) 1 1 and N N (b) 2 4 and N N (c) 1 3 and N N (d) 1 4 and N N 1.6 A linear time invariant system is described by the state variable model 1 1 1 2 2 2 1 0 0 1 2 0 2 1 x x x u x x x - ? ? ? ? ? ? ? ? ? ? = + = ? ? ? ? ? ? ? ? ? ? ? ? ? ? - ? ? ? ? ? ? ? ? ? ? (a) The system is completely controllable (b) The system is not completely controllable (c) The system is completely observable (d) The system is not completely observable 1.7 A process with open-loop model ( ) 4 1 sT ke G s s t - = + is controlled by a PID controller. For this process (a) the integral mode improves transient performance (b) the integral mode improves steady state performance (c) the derivative mode improves transient performance (d) the derivative mode improves steady state performance 1.8 A linear discrete time system has the characteristic equation, 3 0.81 0. z z - = The system (a) is stable (b) is marginally stable (c) in unstable (d) stability cannot be assessed from the given information 2 1 2 1 1 N 1 2 1 1 N 2 2 2 1 1 N 3 1 1 1 1 N 4 2 GATE EC - 1992 1.9 Bode plot of a stable system is shown in figure. The transfer function of the system is _______. 1.10 Given a unity feedback system with open loop transfer function, ( ) ( )( ) . 1 2 K G s s s s = + + The root locus plot of the system is of the form. 1.11 A semiconductor is irradiated with light such that carriers are uniformly generated throughout its volume. The semiconductor is n-type with 19 10 D N = per 3 . cm If the excess electron concentration in the steady state id 15 10 n ? = per 3 cm and if 10 sec p t µ = [minority carrier life time] the generation rate due to irradiation (a) is 20 3 10 pair/cm / e h s - (b) is 24 3 10 pair/cm / e h s - (c) is 10 3 10 pair/cm / e h s - (d) cannot be determined as the given data is insufficient 1.12 A P – N junction in series with a 100 ohms resistor, is forward biased so that a current of 100 mA flows. If the voltage across this combination is instantaneously reversed to 10 V at t = 0, the reverse current that flows through the diode at t = 0 is approximately given by (a) 0 mA (b) 100 mA (c) 200 mA (d) 50 mA dB 20 20 dB/Decade log ? × × × s j? × × × s j? × × × s j? × × × j? s GATE EC - 1992 1.13 An infra red LED is usually fabricated from (a) Ge (b) Si (c) Ga As (d) Ga As P 1.14 In a transistor having finite B, the forward bias across the base emitter junction is kept constant and the reverse bias across the collector base junction is increased. Neglecting the leakage across the collector base junction and the depletion region generating current, the base current will ____. (increase/decrease/remain constant). 1.15 An n-channel JFET has a pinch-off voltage of ( ) 5 , max 20 , p DS V V V V = - = and 2 / . m mA V d = The minimum ‘ON’ resistance is achieved in the JEFT for (a) 7 and 0 GS DS V V V V = - = (b) 7 and 0 GS DS V V V V = = (c) 0 and 20 GS DS V V V V = = (d) 7 and 20 GS DS V V V V = - = 1.16 The JFET in the circuit shown in figure has an 10 and 5 . DSS P I mA V V = = The value of the resistance s R for a drain current 6.4 DS I mA = is (select the nearest value) (a) 150 ohms (b) 470 ohms (c) 560 ohms (d) 1 kilo ohm 1.17 An op.amp has an offset voltage of 1 mV and is ideal in all other respects. If this op.amp is used in the circuit shown in figure, the output voltage will be (select the nearest value) (a) 1 mV (b) 1 V (c) ± 1 V (d) 0 V R S I DS 10V + - - + 1KO 1MO V O Page 5 GATE EC - 1992 Time: 3 hours Maximum Marks: 200 Part A: 80 Marks Part B: 120 Marks 1. This paper consists of two parts: “Part A” and “Part B”. 2. Part A contains 40 questions, each carrying 2 marks. 3. Part B contains 15 questions, each carrying 8 marks. 4. Read the instructions given at the beginning of each part carefully. 5. Attempt ALL questions. 6. There is no negative marking. PART – A 1.1 Relative to a given fixed tree of a network, (a) Link currents form an independent set (b) Branch voltage from an independent set (c) Link currents from an independent set (d) Branch voltage from an independent set 1.2 For a 2-port network to be reciprocal (a) 11 22 z z = (b) 21 12 y y = (c) 21 12 h h = - (d) 0 AD BC - = 1.3 For the series R-L circuit of figure(a), the partial fissure diagram at a certain frequency is shown in figure (b).The operating frequency of the circuit is: (a) equal to the resonance frequency (b) less than the resonance frequency (c) greater than resonance frequency (d) not zero 1.4 For the compensated attenuator of figure, the impulse response under the condition 1 1 2 2 R C R C = is: (a) ( ) 1 1 1 2 1 2 1 R C R e u t R R ? ? - ? ? + ? ? ? ? (b) ( ) 2 1 2 R t R R d + (c) ( ) 2 1 2 R u t R R + (d) ( ) 1 1 1 2 1 2 1 . R C R e u t R R - + + - V + - + - R V L V C V + - (a) R V V C V (b) + - + - C 2 C 1 V 1(t) V 2(t) R 1 R 2(t) C GATE EC - 1992 1.5 Of the four networks, 1 2 3 4 , , and N N N N of figure, the networks having identical driving point functions are (a) 1 1 and N N (b) 2 4 and N N (c) 1 3 and N N (d) 1 4 and N N 1.6 A linear time invariant system is described by the state variable model 1 1 1 2 2 2 1 0 0 1 2 0 2 1 x x x u x x x - ? ? ? ? ? ? ? ? ? ? = + = ? ? ? ? ? ? ? ? ? ? ? ? ? ? - ? ? ? ? ? ? ? ? ? ? (a) The system is completely controllable (b) The system is not completely controllable (c) The system is completely observable (d) The system is not completely observable 1.7 A process with open-loop model ( ) 4 1 sT ke G s s t - = + is controlled by a PID controller. For this process (a) the integral mode improves transient performance (b) the integral mode improves steady state performance (c) the derivative mode improves transient performance (d) the derivative mode improves steady state performance 1.8 A linear discrete time system has the characteristic equation, 3 0.81 0. z z - = The system (a) is stable (b) is marginally stable (c) in unstable (d) stability cannot be assessed from the given information 2 1 2 1 1 N 1 2 1 1 N 2 2 2 1 1 N 3 1 1 1 1 N 4 2 GATE EC - 1992 1.9 Bode plot of a stable system is shown in figure. The transfer function of the system is _______. 1.10 Given a unity feedback system with open loop transfer function, ( ) ( )( ) . 1 2 K G s s s s = + + The root locus plot of the system is of the form. 1.11 A semiconductor is irradiated with light such that carriers are uniformly generated throughout its volume. The semiconductor is n-type with 19 10 D N = per 3 . cm If the excess electron concentration in the steady state id 15 10 n ? = per 3 cm and if 10 sec p t µ = [minority carrier life time] the generation rate due to irradiation (a) is 20 3 10 pair/cm / e h s - (b) is 24 3 10 pair/cm / e h s - (c) is 10 3 10 pair/cm / e h s - (d) cannot be determined as the given data is insufficient 1.12 A P – N junction in series with a 100 ohms resistor, is forward biased so that a current of 100 mA flows. If the voltage across this combination is instantaneously reversed to 10 V at t = 0, the reverse current that flows through the diode at t = 0 is approximately given by (a) 0 mA (b) 100 mA (c) 200 mA (d) 50 mA dB 20 20 dB/Decade log ? × × × s j? × × × s j? × × × s j? × × × j? s GATE EC - 1992 1.13 An infra red LED is usually fabricated from (a) Ge (b) Si (c) Ga As (d) Ga As P 1.14 In a transistor having finite B, the forward bias across the base emitter junction is kept constant and the reverse bias across the collector base junction is increased. Neglecting the leakage across the collector base junction and the depletion region generating current, the base current will ____. (increase/decrease/remain constant). 1.15 An n-channel JFET has a pinch-off voltage of ( ) 5 , max 20 , p DS V V V V = - = and 2 / . m mA V d = The minimum ‘ON’ resistance is achieved in the JEFT for (a) 7 and 0 GS DS V V V V = - = (b) 7 and 0 GS DS V V V V = = (c) 0 and 20 GS DS V V V V = = (d) 7 and 20 GS DS V V V V = - = 1.16 The JFET in the circuit shown in figure has an 10 and 5 . DSS P I mA V V = = The value of the resistance s R for a drain current 6.4 DS I mA = is (select the nearest value) (a) 150 ohms (b) 470 ohms (c) 560 ohms (d) 1 kilo ohm 1.17 An op.amp has an offset voltage of 1 mV and is ideal in all other respects. If this op.amp is used in the circuit shown in figure, the output voltage will be (select the nearest value) (a) 1 mV (b) 1 V (c) ± 1 V (d) 0 V R S I DS 10V + - - + 1KO 1MO V O GATE EC - 1992 1.18 If the transistors in figure, have high values of ß and a BE V of 0.65 volt, the current I, flowing through the 2 kilo ohms resistance will be ______. 1.19. The circuit of figure uses an ideal op amp. For small positive values of , in V the circuit works as (a) a halfwave rectifier (b) a differentiator (c) a logarithmic amplifier (d) an exponential amplifier 1.20. Assume that the operational amplifier in figure is ideal. The current I, through the 1 K ohm resistor is ____. 1.21. The 6 V Zener diode shown in figure has zero zener resistance and a knee current of 5 mA. The minimum value of R so that the voltage across it does not fall below 6 V is: (a) 1.2 K ohms (b) 80 ohms (c) 50 ohms (d) 0 ohms - + I 2K 1kO 2kO 2mA 6.5kO 1.85kO 1.65kO 2kO 1kO I 10V - + V in R - + V out 10V 50O V R - +Read More

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