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GATE 2001 : Electronics And Communication Engineering

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For more files visit www.educationobserver.com/forum SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 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 voltage e0 in figure 1.1 is 4 2 (a) 2V + 4 V (b) 3 4 12V eO - 2 (c) 4V (d) 8V 1.2. If each branch of a Delta circuit has impedance equivalent Wye circuit has impedance. (a) 1.3. Z 3 3Z , then each branch of the (c) 3 3Z (b) 3Z (d) The transfer function of a system is given by H ( s ) = 1 s 2 ( s 2) Z 3 . The impulse response of the system is: (* denotes convolution, and U(t) is unit step function) (a) (t2 * e-2t)U(t) 1.4. (b) (t * e2t)U(t) (c) (te-2t)U(t) (d) (te-2t)U(t) The admittance parameter Y12 in the 2-port network in Figure 1.4 is (a) -0.2 mho 20 I1 (b) 0.1 mho I2 (c) -0.05 mho (d) 0.05 mho E1 5 10 E2 1.5. The region of convergence of the z-transform of a unit step function is (a) z >1 (c) (Real part of z) > 0 (b) z <1 (d) (Real part of z) < 0 For more files visit www.educationobserver.com/forum 1.6. The current gain of a BJT is (a) gmr0 1.7. (b) gm ro (c) gmr (d) gm r MOSFET can be used as a (a) current controlled capacitor (c) current controlled inductor 1.8. (b) voltage controlled capacitor (d) voltage controlled inductor The effective channel length of a MOSFET in saturation decreases with increase in (a) gate voltage (c) source voltage 1.9. (b) drain voltage (d) body voltage The ideal OP-AMP has the following characteristics. (a) Ri = , A = , R0 = 0 (b) Ri = 0, A = , R0 = 0 (c) Ri = , A = , R0 = (d) Ri = 0, A = , R0 = 1.10. The 2 s complement representation of 17 is (a) 01110 (b) 01111 (c) 11110 (d) 10001 1.11. Consider the following two statements: Statement 1: A stable multi-vibrator can be used for generating square wave. Statement 2: B stable multi-vibrator can be used for storing binary information. (a) Only statement 1 is correct (b) Only statement 2 is correct (c) Both the statements 1 and 2 are correct (d) Both the statements 1 and 2 are incorrect 1.12. For the ring oscillator shown in Figure 1.12, the propagation delay of each inverter is 100 pico second. What is the fundamental frequency of the oscillator output? (a) 10 MHz V0 (b) 100 MHz (c) 1 GHz (d) 2 GHz 1.13. An 8085 microprocessor based system uses a 4K 8-bit RAM whose starting address is AA00. The address of the last byte in this RAM is (a) 0FFFH (b) 1000 H (c) B9FF H (d) BA00 H For more files visit www.educationobserver.com/forum 1.14. The equivalent of the block diagram in Figure 1.14 is given in E F (a) E G1 H G1 G2 C (b) C E F E G1 G1G2 C HG2 F 15. HG2 (d) C E F C H/G2 F (c) G1G2 H/G2 If the characteristic equation of a closed-loop system is s2 + 2s + 2 = 0 , then the system is (a) over damped (b) critically damped (c) underdamped (d) undamped 1.16. The root-locus diagram for a closed loop feedback system is shown in Figure 1.16. The system is overdamped. j K=5 K= K=0 x K -3 -2 K=0 x -1 K=1 (a) only if 0 K 1 (b) only if 1 < K < 5 (c) only if K > 5 (d) if 0 K < 1 or K > 5 For more files visit www.educationobserver.com/forum 1.17. The Nyquist plot for the open-loop transfer function G(s) of a unity negative feedback system is shown in figure 1.17 if G(s) has no pole in the right half of splane, the number of roots of the system characteristic equation in the right half of s-plane is Im(s) (a) 0 (b) 1 G(s)-Plane (c) 2 (d) 3 -1 Re(s) 1.18. Let (t) denote the delta function. The value of the integral 3t dt is (t ) cos 2 (a) 1 (b) -1 (c) 0 (d) 2 1.19. A band limited signal is sampled at the Nyquist rate. The signal can be recovered by passing the samples through (a) an RC filter (b) an envelope detector (c) a PLL (d) an ideal low-pass filter with appropriate bandwidth 2 1.20. The PDF of a Gaussian random variable X is given by Px ( x ) = ( x 4) 1 3 2 e 18 probability of the event {X = 4} is (a) 1 2 (b) 1 3 2 (c) 0 (d) 1 4 1.21. If a signal f(t) has energy E, the energy of the signal f(2t) is equal to (a) E (b) E 2 (c) 2E (d) 4E (c) LG = RC (d) RG = LC 1.22. A transmission line is distortion-less if (a) RL = 1 GC (b) RL = GC . The For more files visit www.educationobserver.com/forum 1.23. If a plane electromagnetic wave satisfies the equation 2 E x x 2 = c2 2 E x t 2 , the wave propagates in the (a) x-direction (b) z-direction (c) y-direction (d) xy plane at an angle of 45 between the x and z directions 1.24. The phase velocity of waves propagating in a hollow metal waveguide is (a) greater than the velocity of light in free space. (b) less than the velocity of light in free space. (c) equal to the velocity of light in free space. (d) equal to the group velocity. 1.25. The dominant mode in a rectangular waveguide is TE10, because this mode has (a) no attenuation (b) no cut-off (c) no magnetic field component (d) the highest cut-off wavelength 2. This question consists of TWENTY-FIVE sub-questions (2.1 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 2.1 The voltage e0 in figure 2.1 is (a) 48 V 2.2. (b) 24 V 8A (c) 36 V 16V (d) 28 V 12 10 6 + e0 - In figure 2.2, the value of the load resistor R which maximizes the power delivered to it is 1H 10 (a) 14.14 (b) 10 (c) 200 (d) 28.28 Emcos10t ~ R For more files visit www.educationobserver.com/forum 2.3. When the angular frequency in Figure 2.3 is varied from 0 to , the locus of the current phasor I2 is given by i(t) i1(t) Emcos t i2(t) 16V R2 R1 ~ C (a) (b) Em 2R2 =0 I2 = Em 2R2 Em 2R2 = (c) (d) Em R1 Em 2R2 I2 =0 = Em R1 2.4 Em 2R2 Em 2R2 E = Em 0 E = Em 0 =0 Em 2R2 I2 = The Z parameters Z11 and Z21 for the 2-port network in figure 2.4 are (a) Z11 = (b) Z11 = 6 16 ; Z21 = ; 11 11 6 4 ; Z21 = ; 11 11 (c) Z11 = I1 2 I2 4 E1 6 16 ; Z21 = ; 11 11 (d) Z11 = 2.5 I2 E = Em 0 Em 2R2 E = Em 0 =0 E2 10E1 4 4 ; Z21 = ; 11 11 An npn BJT has gm = 38m A/V, C =10-14 F, C =4 10-13F, and DC current gain 0 = 90. for this transistor fT and f are (a) fT = 1.64 108 Hz and f = 1.47 1010 Hz (b) fT = 1.47 1010 Hz and f = 1.64 108 Hz For more files visit www.educationobserver.com/forum (c) fT = 1.33 1012 Hz and f = 1.47 1010 Hz (d) fT = 1.47 1010 Hz and f = 1.33 1012 Hz 2.6 The transistor shunt regulator shown in Figure 2.6 has a regulated output voltage of 10 V, when the input varies from 20 V to 30 V. The relevant parameters for the Zener diode and the transistor are: Vz = 9.5, VSE=0.3V, =99. Neglect the current through RB. Then the maximum power dissipated in the Zener diode (Pz) and the transistor (PT) are 20 IZ IC VZ Vin=20-30V VO=10V VBE+ RB (a) PZ=75mW, PT=7.9W (c) PZ=95mW, PT=9.9W 2.7 (b) PZ=85mW, PT=8.9W (d) PZ=115mW, PT=11.9W The oscillator circuit shown in Figure 2.7 is -VCC LC L=10 H CC Vo R1 C1 = 2pF R2 Re C2= 2pF Ce (a) Hartley oscillator with foscillation = 79.6MHz (b) Colpitts oscillator with foscillation = 79.6MHz (c) Hartley oscillator with foscillation = 159.2MHz (d) Colpitts oscillator with foscillation = 159.2MHz 2.8 The inverting OP-AMP shown in Figure 2.8 has an open-loop gain of 100. The v closed loop gain 0 is vs (a) -8 (b) -9 R2=10K R1=1K Vs (c) -10 Vi + - + Vo (d) -11 For more files visit www.educationobserver.com/forum 2.9 In Figure 2.9, assume the OP-AMPs to be ideal. The output v0 of the circuit is: 10mH 10 F 10 100 Vs - Vs=10cos(100t) - + VO + t (b) 10 cos (100 ) d (a) 10 cos(100t) 0 t (c) 10 4 cos (100 ) d (d) 10 4 0 2.10 d cos (100t ) dt In Figure 2.10, the LED VCC=5V 1K 1K 1K LED 1K S1 S2 (a) emits light when both S1 and S2 are closed. (b) emits light when both S1 and S2 are open. (c) emits light when only S1 or S2 is closed. (d) does not emit light, irrespective of the switch positions. 2.11 In the TTL circuit in Figure 2.11, S2 to S0 are select lines and X7 and X0are input lines. S0 and X0 are LSBs. The output Y is (a) indeterminate (b) A B (c) A B (d) C. A B + C. ( A B ) ( ) For more files visit www.educationobserver.com/forum 1 0 x0 x1 x2 x3 x6 x7 x5 x4 E B S2 S1 A S0 C Fig.2.11 y 2.12 The digital block in figure 2.12 is realized using two positive edge triggered Dflip-flops. Assume that for t < t0, Q1 = Q2 =0. The circuit in the digital block is given by: Y X DIGITAL BLOCK t0 t1 t2 t0 t3 t1 t2 (a) Figure 2.12 (a) 1 (b) Figure 2.12 (b) (c) Figure 2.12 (c) (d) Figure 2.12 (d) D1 X Q1 1 D2 Q2 Y X Q2 Q1 1 D1 O Q1 X D1 Q1 Q1 Figure (c) 1 D2 O Q1 Q2 Y Q2 Figure (b) Figure (a) 1 t4 t3 D2 Q2 Q2 Y 1 X D1 O Q1 D2 O Q1 Figure (d) Q2 Q2 Y For more files visit www.educationobserver.com/forum 2.13 In the DRAM cell in Figure 2.13, the Vt of the NMOSFET is 1 V. For the following three combinations of WL and BL voltages. Word Line (WL) Bit Line (BL) C (a) 5 V; 3V; 7V 2.14 (b) 4 V; 3V; 4V (c) 5 V; 5V; 5V (d) 4 V; 4V; 4V The impulse response functions of four linear systems S1, S2, S3, S4 are given respectively by h1 ( t ) = 1 h2 ( t ) = U ( t ) h3 ( t ) = U (t ) t +1 h4 ( t ) = e 3t U ( t ) where U(t) is the unit step function. Which of these systems is time invariant, causal, and stable? (a) S1 2.15 (b) S2 (c) S3 (d) S4 An electrical system and its signal-flow graph representations are shown in Figure 2.15(a) and 2.15(b) respectively. The values of G2 and H, respectively are (a) (b) (c) (d) Z3 ( s ) , Z3 ( s ) Z2 ( s ) + Z3 ( s ) + Z4 ( s ) Z1 ( s ) + Z3 ( s ) Z3 ( s ) , Z3 ( s ) Z2 ( s ) Z3 ( s ) + Z4 ( s ) Z1 ( s ) + Z3 ( s ) Z3 ( s ) , Z3 ( s ) Z2 ( s ) + Z3 ( s ) + Z4 ( s ) Z1 ( s ) + Z3 ( s ) Z3 ( s ) , Z3 ( s ) Z2 ( s ) Z3 ( s ) + Z4 ( s ) Z1 ( s ) + Z3 ( s ) For more files visit www.educationobserver.com/forum Vo(s) Z2(s) Z1(s) I1(s) I2(s) Z3(s) Figure (b) Z4(s) Vi(s) G1 I1(s) G2 I2(s) G3 Vi(s) Vo(s) Figure (a) H 2.16 The open-loop DC gain of a unity negative feedback system with closed-loop s+4 transfer function 2 is s + 7s + 13 (a) 2.17 4 13 (b) 4 9 (c) 4 The feedback control system in Figure 2.17 is stable (a) for all K 0 (b) only if K 1 S 2 + R(s) 2 K 0 (d) only if 0 K 1 (b) 100 Mbps (c) 600 Mbps (d) 6.4 Gbps The Nyquist sampling interval, for the signal Sinc (700t) + Sinc (500t) is (a) 2.20 S K- 2 A video transmission system transmits 625 picture frames per second. Each frame consists of a 400 400 pixel grid with 64 intensity levels per pixel. The data rate of the system is (a) 16 Mbps 2.19 C(s) ( S + 2) - (c) only if 0 K < 1 2.18 (d) 13 1 sec 350 (b) 350 sec (c) 1 sec 700 (d) 175 sec During transmission over a communication channel, bit errors occur independently with probability p. If a block of n bits is transmitted, the probability of at most one bit error is equal to (a) 1 (1 p)n (c) np(1 p) n-1 (b) p + (n 1) ( 1 p) (d) (1 p)n + np(1 p)n-1 For more files visit www.educationobserver.com/forum 2.21 The PSD and the power of a signal g(t) are, respectively, Sg( ) and Pg. The PSD and the power of the signal ag(t) are, respectively (a) a2 Sg ( ) and a2 Pg (c) aSg ( ) and a2 Pg 2.22 (b) a2 Sg ( ) and aPg (d) aSg ( ) and aPg A material has conductivity of 10-2 mho/m and a relative permittivity of 4. The frequency at which the conduction current in the medium is equal to the displacement current is (a) 45 MHz 2.23 (b) 90 MHz (b) 25% (c) 50% (d) 75% A medium wave radio transmitter operating at a wavelength of 492 m has a tower antenna of height 124m. What is the radiation resistance of the antenna? (a) 25 2.25 (d) 900 MHz A uniform plane electromagnetic wave incident normally on a plane surface of a dielectric material is reflected with a VSWR of 3. What is the percentage of incident power that is reflected? (a) 10% 2.24 (c) 450 MHz (b) 36.5 (c) 50 (d) 73 In a uniform linear array, four isotropic radiating elements are spaced apart. 4 The progressive phase shift between the elements required for forming the main beam at 60 off the end-fire is: (a) - radians (b) 2 radians (c) 4 radians (d) 8 radians SECTION B This section consists of TWENTY questions of FIVE marks each. Attempt ANY FIFTEEN questions. Answers must be given in the answer book provided. 3. For the circuit shown in figure 3, determine the phasors E2, E0, I and I1. 1 I 0.5 E1 j2 I1 E1=10 20 ~ -j 1 0.5 E0 For more files visit www.educationobserver.com/forum 4. The circuit shown in Figure 4 is operating in steady-state with switch S1 closed. The switch S1 is opened at t = 0. (a) Find iL(0+). (b) Find e1(0+). (c) Using nodal equations and Laplace transform approach, find an expression for the voltage across the capacitor for all t > 0. 2 2 e1(t) 5 e2(t) S1 iL(t) 15V 5. C= L=0.5H 1 F 8 10V The admittance parameters of a 2-port network shown in figure 5 are given by Y11 = 2 mho, Y12 = -0.5 mho, Y21 = 4.8 mho, Y22 = 1 mho. The output port is terminated with a load admittance YL = 0.2 mho. Find E2 for each of the following conditions? (a) E1=10 0 V (b) I1=10 0 A (c) A source 10 0 V in series with a 0.25 resistor is connected to the input port. 6. For the circuit shown in figure 6, D1 and D2 are indentical diodes with idealilty factor of unity. The thermal voltage VT = 25 mV. (a) Calculate Vf and Vr. (b) If the reverse saturation current, Is, for the diode is 1 pA, then compute the current I through the circuit. D1 D2 - + - + Vf Vr I 50mV For more files visit www.educationobserver.com/forum 7. An emitter-follower amplifier is shown in Figure 7. Zi is the impedance looking into the base of the transistor and Z0 is the impedance looking into the emitter of the transistor. (a) Draw the small signal equivalent circuit of the amplifier. (b) Obtain an expression for Zi. (c) Obtain an expression for Z0. (d) Determined Zi and Z0 if a capacitor CL is connected across RL. VCC IC RS Zo Vo Zi + VS RL - -VEE 8. Assume that the OP-AMP in Figure 8 is ideal. (a) obtain an expression for vo in terms of vs, R, and the reverse saturation current Is of the transistor. (b) If R = 1 , Is = 1 pA and the thermal voltage VT = 25 mV, then what is the value of the output voltage vo for an input voltage vs = 1V? (c) Suppose that the transistor in the feedback path is replaced by a p-n junction diode with a reverse saturation current of Is. The p-side of the diode is connected to node A and the n-side to node B. Then what is the expression for vo in terms of vs, R and Is? R VS + - 9. A + B + Vo - A monochrome video signal that ranges from 0 to 8V, is digitized using an 8-bit ADC. (a) Determine the resolution of the ADC in V/bit. (b) Calculate the mean squared quantization error. (c) Suppose the ADC is counter controlled. The counter is up count and positive edge triggered with clock frequency 1 MHz. What is the time taken in seconds to get a digital equivalent of 1.59 V? For more files visit www.educationobserver.com/forum 10. In figure 10, the output of the oscillator, V1 has 10V peak amplitude with zero DC value. The transfer characteristic of the Schmitt inverter is also shown in figure 10. Assume that the JK flip-flop is resent at time t = 0. (a) What is the period and duty cycle of the waveform V2? (b) What is the period and duty cycle of the waveform V3? (c) Sketch V1, V2 and V3 for the duration 0 t 6 s. Clearly indicate the exact timings when the waveforms V2 and V3 make high-to-low and low-to-high transitions. VCC=5V J 0.5 MHz sinewave oscillator V1 Q V2 V2 K 5V oscillator J-K flip-flop Schmitt inverter 0V V1 2.5V 3.5V 11. For the digital block shown in Figure 11(a), the output Y=f(S3,S2,S1,S0) where S3 is MSB and S0 is LSB. Y is given in terms of minterms as Y = m (1,5, 6,7,11,12,13,15) and its complement is Y = m ( 0, 2, 3, 4, 8, 9,10,14 ) (a) Enter the logical values in the given Karnaugh map [Fig.11(b)] for the output Y. (b) Write down the expression for Y in sum-of products from using minimum number of terms (c) Draw the circuit for the digital logic boxes using four 2-input NAND gates only for each of the boxes. S1S0 S1 S3 S0 S3S2 S2 00 DIGITAL DIGITAL LOGIC BOX 2 01 LOGIC BOX 1 Y 11 10 00 01 11 10 For more files visit www.educationobserver.com/forum 12. Consider the following sequence of instructions for an 8085 microprocessor based system. Memory address FF00 FF02 FF03 FF06 FF08 FF0B FF0C FF0E FF10 FF12 FF14 FF15 FF17 FF19 FF1A FF1D FF20 FF23 FF24 FF26 Instructions MVI, A INR A JC ORI JM XRA A OUT HLT XRI OUT HLT MVI, A ADI RAL JZ JC JNC CMA OUT HLT FF H FF0C H A8H FF15 H PORT 1 FF H PORT 2 FF H 02 H FF23 H FF10 H FF12 H PORT 3 (a) If the program execution begins at the location FF00 H, write down the sequence of instructions which are actually executed till a HLT instruction. (Assume all flags are initially RESET) (b) Which of the three ports (PORT1, PORT2 and PORT3) will be loaded with data and what is the bit pattern of the data? 13. A feedback control system is shown in figure 13. (a) Draw the signal-flow graph that represents the system. (b) Find the total number of loops in the graph and determine the loop-gains of all the loops. (c) Find the number of all possible combination of non-touching loops taken two at a time. (d) Determine the transfer function of the system using the signal-flow graph. For more files visit www.educationobserver.com/forum + + + G1 R(s) G2 - - + C(s) - Fig.13 14. Consider the feedback control system shown in figure 14. (a) Find the transfer function of the system and its characteristic equation. (b) Use the Routh-Hurwitz criterion to determine the range of K for which the system is stable. R(s) + K ( s + 1) - + s 1 2 - C(s) 3 1 s + 0.1 15. For the feedback control system shown in figure 15, the process transfer function 1 is Gp ( s ) = , and the complification factor of the power amplifier is K 0. s ( s + 1) The design specifications required for the system are a time constant of 1 sec and a damping ratio of 0.707. (a) Find the desired locations of the closed loop poles. (b) Write down the required characteristic equation for the system. Hence determine the PD controller transfer function G0 ( s ) when K = 1. (c) Sketch the root-locus for the system. R(s) + PD controller - Power amplifier Process C(s) For more files visit www.educationobserver.com/forum 16. The Fourier transform G( ) of the signal g(t) in Figure 16(a) is given as 1 G ( ) = 2 e j j e j 1 . Using this information and the time-shifting and ( ) time-scaling properties, determine the Fourier transform of signals in Figures 16(b), 16(c) and 16(d). g(t) 1 -1 g1(t) 1 t 0 g2(t) 17. g2(t) 1 -1 t 1 0 1 t 0 - t 1 01 2 2 The periodic modulating signal m(t) is shown in Fig.17. Using Carson s rule estimate BFM (bandwidth of the FM signal) and BPM (bandwidth of the PM signal) for Kf = 104 and kp = . Assume the essential bandwidth of m(t) to consist 4 only up to and including the third harmonic. m(t) 2 10-4 1 t (sec) -1 For more files visit www.educationobserver.com/forum 18. A baseband signal g(t) bandlimited to 100 Hz modulates a carrier of frequency f0 Hz. The modulated singal g(t)cos 2 f t is transmitted over a channel whose input x and output y are related by y = 2x + x2. The spectrum of g(t) is shown in Figure 18. Sketch the spectrum of the transmitted signal and the spectrum of the received signal. G(f) 1 f(Hz) -100 19. 100 0 A periodic signal g(t) is shown in Figure 19. Determine the PSD of g(t). g(t) -2 - 2 2 t 2 4 sec 20. A system of three electric charges lying in a straight line is in equilibrium. Two of the charges are positive with magnitudes Q and 2Q, and are 50 cm apart. Determine the sign, magnitude and position of the third charge. 21. A medium has breakdown strength of 16 KV/m r.m.s. Its relative permeability is 1.0 and relative permittivity is 4.0 A plane electromagnetic wave is transmitted through the medium. Calculate the maximum possible power flow density and the associated magnetic filed. 22. A rectangular hollow metal waveguide has dimensions a= 2.29 cm and b = 1.02 cm. Microwave power at 10 GHz is transmitted through the waveguide in the TE10 mode. (a) Calculate the cut-off wavelength and the guide wavelength for this mode. (b) What are the other (TE or TM) modes that can propagate through the waveguide? (c) If a = b = 2.29cm, What are the modes which can propagate through the waveguide?

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