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GATE 1998 : Electronics And Communication Engineering

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For more files visit www.educationobserver.com/forum 1. For each of the following (1.1 1.40) four alternatives (A, B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer by writing (A, B, C or D) as appropriate, against the corresponding question number in the answer book. 1.1 A network has 7 nodes and 5 independent loops. The number of branches in the network is (a) 13 1.2 (b) 12 (d) 10 0 1 The eigen values of the matrix A = are 1 0 (a) 1,1 1.3 (c) 11 If f ( t ) = (b) -1,-1 2 s + 2 (c) j,-j (d) 1,-1 , then the value of lim f ( t ) t (a) cannot be determined (c) is unity 1.4 (b) is zero (d) is infinite The trigonometric Fourier series of a periodic time function can have only (a) cosine terms (c) cosine and sine terms 1.5 (b) sine terms (d) d.c. and cosine terms The nodal method of circuit analysis is based on (a) KVL and Ohm s law (c) KCL and KVL 1.6 (b) KCL and Ohm s law (d) KCL, KVL and Ohm s law Superposition theorem is NOT applicable to networks containing (a) nonlinear elements (c) dependent current sources 1.7 (b) dependent voltage sources (d) transformers The parallel RLC circuit shown in Fig.1.7 is in resonance. In this cicuit (a) IR < 1mA (b) IR + IL > 1mA (c) IR + IC < 1mA (d) IR + IC > 1mA IR 1mA RMS IL R L IC Join All India Mock GATE Classroom Test Series - 2007 conducted by GATE Forum in over 25 cities all over India. Question Papers including section tests and full tests are designed by IISc alumni according to the latest syllabus. Percentile, All India Rank, interaction with IISc alumni in our online discussion forums, and more. For more details, visit www.gateforum.com Think GATE Think GATE Forum For more files visit www.educationobserver.com/forum GATE EC - 1998 www.gateforum.com Join discussion of this test paper at http://forum.gatementor.com 1.8 A periodic signal x(t) of period To is given by 1, t < T1 x (t ) = To 0, T1 < t < 2 The d.c. component of x(t) is (a) 1.9 T1 T0 (b) T1 2T0 (c) 2T1 T0 (d) T0 T1 The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of the system ot an excitation e at u ( t ) , a > 0 will be 1 (b) 1 e at a ( (a) ae at 1.10 ) ( (c) a 1 e at ) (d) 1 e at 0 The short-circuit admittance matrix of a two-port network is 1 2 1 2 0 The two port network is (a) non-reciprocal and passive (c) reciprocal and passive 1.11 (b) non-reciprocal and active (d) reciprocal and active The voltage across the terminals a and b in Fig.1.11 is (a) 0.5 V 2 1 a (b) 3.0 V (c) 3.5 V + 1V (d) 4.0 V 2 3A 1H t 1.12 The electron and hole concentrations in a intrinsic semiconductor are ni and pi respectively. When doped with a p-type material, these change to n and p, respectively. Then (a) n + p = ni + pi 1.13 (b) n + ni = p + pi (c) npi = ni p (d) np = ni pi If fT of BJT is related to its gm , C and C as follows: (a) fT = (c) fT = C + C gm gm C + C (b) fT = (d) fT = ( e C + C gm gm 2 C + C ) For more files visit www.educationobserver.com/forum 1.14 The static characteristic of an adequately forward biased p-n junction is a straight line, if the plot is of (a) log I vs. log V 1.15 (b) log I vs. V (c) I vs. log V (d) I vs. V A long specimen of p-type semiconductor material (a) is positively charged (b) is electrically neutral (c) has an electric field directed along its length (d) acts as a dipole 1.16 The Z-transform of the time function ( n k ) is k =0 (a) 1.17 Z 1 Z (b) (c) Z (d) ( Z 1)2 ( Z 1)2 Z The number of roots of s3 + 5s2 + 7s + 3 = 0 in the left half of the s-plane is (a) zero 1.18 Z Z 1 (b) one (c) two (d) three The transfer function of a tachometer is of the form (a) Ks (b) K s (c) K s ( + 1) (d) K s ( s + 1) 1.19. Consider a unity feedback control system with open-loop transfer function K . The steady state error of the system due to a unit step input is G (s) = s ( s + 1) (a) zero (b) K (c) 1 K (d) infinite 1.20. The transfer function of a zero-order-hold system is 1 (a) 1 + e sT s ( 1 (b) 1 e sT s ) ( 1 (c) 1 e sT s ) 1 (d) 1 + e sT s 1.21. In the Bode-plot of a unity feedback control system, the value of phase of G(j ) at the gain cross over frequency is 125 . The phase margin of the system is (a) -125 (b) -55 (c) 55 (d) 125 For more files visit www.educationobserver.com/forum 1.22. Consider a feedback control system with loop transfer fucntion G (s) H (s) = K (1 + 0.5s ) s (1 + s ) (1 + 2s ) The type of the closed loop system is (a) zero (b) one (c) two 1.23. The transfer function of a phase lead controller is (d) three 1 + 3Ts . The maximum value of 1 + Ts phase provided by this controller is (a) 90 (b) 60 (c) 45 (d) 30 1.24. The Nyquist plot of a phase transfer function g(j ) H(j ) of a system encloses the (-1,0) point. The gain margin of the system is (a) less than zero (c) greater than zero 1.25 (b) zero (d) infinity The transfer function of a system is 2s 2 + 6 s + 5 ( s + 1)2 ( s + 2) The characteristic equation of the system is (a) 2s2 + 6s + 5 = 0 (b) 2 (c) 2s2 + 6s + 5 + ( s + 1) 1.26 2 (d) 2s2 + 6s + 5 ( s + 1) ( s + 2) = 0 n In a synchro error detector, the output voltage is proportional to ( t ) , where ( t ) is the rotor velocity and n equals (a) -2 1.27 ( s + 2) = 0 ( s + 1)2 ( s + 2) = 0 (b) -1 (c) 1 (d) 2 Two identical FETs, each characterissed by the parameters gm and rd are connected in parallel. The composite FET is then characterized by the parameters (a) 1.28 gm and 2rd 2 (b) r gm and d 2 2 (c) 2gm and VO (a) current series (b) current shunt (d) voltage shunt (d) 2gm and 2rd +VCC The circuit of Fig.1.28 is an example of feedback of the following type (c) voltage series rd 2 Vi ~ For more files visit www.educationobserver.com/forum 1.29 In a differential amplifier, CMRR can be improved by using an increased (a) emitter resistance (c) power supply voltages 1.30 (b) collector resistance (d) source resistance From a measurement of the rise time of the output pulse of an amplifier whose input is a small amplitude square wave, one can estimate the following parameter of the amplifier: (a) gain-bandwidth product (c) upper 3-dB frequency 1.31 (b) slow rate (d) lower 3-dB frequency A distorted sinusoidal has the amplitudes A1 , A2 , A3 K of the fundamental, second harmonic, third harmonic, K respectively. The total harmonic distortion is (a) A2 + A3 + K A1 (c) 1.32 A22 + A32 + K (b) A1 2 A2 + A3 + K (d) 2 A1 A22 + A32 + K 2 A12 + A22 + A3 K The emitter coupled pair of BJT s gives a linear transfer relation between the differential output voltage and the differential input voltage Vid only when the magnitude of Vid is less times the thermal voltage, where is (a) 4 1.33 (b) 3 (c) 2 (d) 1 In a shunt-shunt negative feedback amplifier, as compared to the basic amplifier (a) both, input and output impedances, decrease (b) input impedance decreases but output impedance increases (c) input impedance increases but output impedance decreases (d) both, input and output impedances increase 1.34 A multistage amplifier has a low-pass response with three real poles at s = - 1, - 2 and 3. The approximate overall bandwidth B of the amplifier will be given by (a) B = 1 + 2 + 3 (b) 1 (c) B = ( 1 + 2 + 3 ) 3 1 1 1 1 = + + B 1 2 3 2 2 2 (d) B = 1 + 2 + 3 For more files visit www.educationobserver.com/forum 1.35 A high Q-quartz crystal exhibits series resonance at the frequency s and parallel resonance at the frequency p . Then (a) s is very close to, but less than p . p. (c) s is very close to, but greater than p . 1.36 (b) s (d) s p. One input terminal of high gain comparator circuit is connected to ground and a sinusoidal voltage is applied to the other input. The output of comparator will be (a) a sinusoid (c) a half rectified sinusoid 1.37 (b) a full rectified sinusoid (d) a square wave In a series regulated power supply circuit, the voltage gain Av of the pass transistor satisfies the condition: (a) Av 1.38 (b) 1 (c) Av =1 Av < (d) Av 1 For full wave rectification, a four diode bridge rectifier is claimed to have the following advantages over a two diode circuit: (1) less expensive transformer (2) smaller size transformer, and (3) suitability for higher voltage application. Of these, (a) only (1) and (2) are true (c) only (2) and (3) are true 1.39 (b) only (1) and (3) are true (d) (1), (2) as well as (3) are true In the MOSFET amplifier of Fig.1.39, the signal outputs V1 and V2 obey the relationship (a) V1 = V2 2 RD V (b) V1 = 2 2 + (c) V1 = 2V2 Vi (d) V1 = 2V2 1.40 the units of (a) V ~ RD 2 + V2 - + V1 - - q are kT (b) V 1 (c) J (d) J K For more files visit www.educationobserver.com/forum 2. For each of the following (2.1 2.40) four alternatives (A, B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer by writing (A, B, C or D) as appropriate, against the corresponding question number in the answer book. 2.1 The minimum number of 2-input NAND gates required to implement the Boolean function Z = A B C , assuming that A, B and C are available, is (a) two 2.2 (c) five (d) six (c) 0.6 V (d) 0.8 V The noise margin of a TTL gate is about (a) 0.2 V 2.3 (b) three (b) 0.4 V In Fig.2.3, A = 1 and B =1, the input B is now replaced by a sequence 101010 . the outputs x and y will be (a) fixed at 0 and 1, respectively A X (b) x = 1010 . while y = 0101 . (c) x = 1010 . and y = 0101 . (d) fixed at 1 and 0, respectively Y B 2.4 An equivalent 2 s complement representation of the 2 s complement number 1101 is (a) 110100 2.5 (b) 001101 (c) 110111 (d) 111101 The threshold voltage for each transistor in Fig.2.5, is 2V. For this circuit to work as an inverter, Vi must take the values (a) -5 V and 0 V (b) -5 V and 5 V (c) -0 V and 3 V (d) 3 V and 5 V 2.6 VO Vi An I/O processor control the flow of information between -5V (a) cache memory and I/O devices (b) main memory and I/O devices (c) two I/O devices (d) cache and main memories For more files visit www.educationobserver.com/forum 2.7 Two 2 s complement number having sign bits x and y are added and the sign bit of the result is z. Then, the occurrence of overflow is indicated by the Boolean function (a) x y z (c) x y z + x y z 2.8 (b) x y z (d) xy + yz + zx The advantage of using a dual slope ADC in a digital voltmeter is that (a) its conversion time is small (c) it gives output in BCD format 2.9 (b) its accuracy is high (d) it does not require a comparator For the identify AB + AC + BC = AB + AC , the dual form is (a) ( A + B) ( A + C ) (B + C ) = ( A + B) ( A + C ) (b) ( A + B ) ( A + C )( B + C ) = ( A + B ) ( A + C ) ( A + B) ( A + C ) (B + C ) = ( A + B ) ( A + C ) (c) (d) A B + A C + B C = A B + A C 2.10 An instruction used to set the carry Flag in a computer can be classified as (a) data transfer (c) logical 2.11 (b) arithmetic (d) program control Fig.2.11 shows a mod-K counter, here K is equal to J Q K (a) 1 Q (b) 2 (c) 3 Q J 1 K Q (d) 4 CLK 2.12 The current I through resistance r in the circuit shown in Fig.2.12 is r I R R 2R R R 2R 2R V 0 (a) V 12R (b) V 12R + 2R 0 (c) V 6R (d) V 3T For more files visit www.educationobserver.com/forum 2.13 The K-map for a Boolean function is shown in Fig.2.13. The number of essential prime implicants for this function is AB (a) 4 CD (b) 5 00 01 11 10 00 1 1 0 1 01 0 0 0 1 11 1 0 0 0 1 0 0 1 (c) 6 (d) 8 10 2.14 For small signal a.c. operation, a practical forward biased diode can be modeled as (a) a resistance and a capacitance in series (b) an ideal diode and resistance in parallel (c) a resistance and an ideal diode in series (d) a resistance 2.15 The amplitude spectrum of a Gaussian pulse is (a) uniform (c) Gaussian 2.16 (b) a sine function (d) an impulse function The ACF of a rectangular pulse of duration T is (a) a rectangular pulse of duration T (b) a rectangular pulse of duration 2T (c) a triangular pulse of duration T (d) a triangular pulse of duration 2T 2.17 The image channel selectivity of super heterodyne receiver depends upon (a) IF amplifiers only (b) RF and IF amplifiers only (c) Preselector, RF and IF amplifiers (d) Preselector, and RF amplifiers only 2.18 In a PCM system with uniform quantization, increasing the number of bits from 8 to 9 will reduce the quantization noise power by factor of (a) 9 (b) 8 (c) 4 (d) 2 For more files visit www.educationobserver.com/forum 2.19 The Fourier transform of a function x(t) is X(f). The Fourier transform of dX ( f ) will be df (a) 2.20 dX ( f ) df (b) j2 fX ( f ) (c) jfX ( f ) (d) X (f ) jf Flat top sampling of low pass signals (a) gives rise to aperture effect (c) leads to aliasing 2.21 (b) implies over sampling (d) introduces delay distortion A DSB-SC signal is generated using the carrier cos ( et + ) and modulating singal x(t). The envelope of the DSB-SC signal is x (t ) (a) x(t) (c) only positive portion of x(t) 2.22 (b) (d) x(t) cos Quadrature multiplexing is (a) the same as FDM (b) the same as TDM (c) a combination of FDM and TDM (d) quite different from FDM and TDM 2.23 The Fourier transform of a voltage signal x(t) is X(f). The unit of X ( f ) is (a) volt 2.24 (b) volt-sec (c) volt/sec (d) volt2 Compression in PCM refers to relative compression of (a) higher signal amplitudes (c) lower signal frequencies 2.25 (b) lower signal amplitudes (d) higher signal frequencies For a given data rate, the bandwidth Bp of a BPSK signal and the bandwidth B0 of the OOK signal are related as (a) Bp = 2.26 B0 4 (b) Bp = B0 2 (c) Bp = B0 (d) Bp = 2B0 The spectral density of a real valued random process has (a) an even symmetry (c) a conjugate symmetry 2.27 (b) an odd symmetry (d) no symmetry The probability density function of the envelope of narrow band Gaussion noise is (a) Poisson (b) Gaussian (c) Rayleigh (d) Rician For more files visit www.educationobserver.com/forum 2.28 The intrinsic impedance of copper at high frequencies is (a) purely resistive (b) purely inductive (c) complex with a capacitive component (d) complex with an inductive component 2.29 The Maxwell equation V H = J D is based on t (a) Ampere s law (b) Gauss law (c) Faraday s law (d) Coulomb s law 2.30 All transmission line sections shown in Fig.2.30 have characteristic impedance Ro + j0. The input impedance 8 2 2R0 Zin Zin equals (a) (b) Ro (c) 2.31 2 Ro 3 3 Ro 2 (d) 2Ro The time averages Poynting vector, ur u r j t + z ) E = 24e ( ay V/m in free space is (a) 2.32 2 0.05 m r 2.4 u az W/m2, in (c) r 4.8 u az for a (d) wave with r 4.8 u az (b) 10 m (c) 20 m (d) 30 m The depth of penetration of wave in a lossy dielectric increases with increasing (a) conductivity 2.34 (b) 1 4 The wavelength of a wave with propagation constant (0.1 +j0.2 )m-1 is (a) 2.33 r 2.4 u az Ro 2 (b) permeability (c) wavelength (d) permittivity ur u r u r j t + z ) ax + ay is The polarization of wave with electric field vector E = E0e ( ( (a) linear (b) elliptical (c) left hand circular (d) right hand circular ) For more files visit www.educationobserver.com/forum 2.35 The vector H in the far field of an antenna satisfies uu r uu r uu r uu r (a) .H = 0 and H = 0 (b) .H 0 and H 0 uu r uu r uu r uu r (c) .H = 0 and H 0 (d) .H 0 and H = 0 2.36 The radiation resistance of a circular loop of one turn is 0.01 . The radiation resistance of five turns of such a loop will be (a) 0.002 2.37 (c) 0.05 (d) 0.25 An antenna in free space receives 2 W of power when the incident electric field is 20 mV/m rms. The effective aperture of the antenna is (a) 0.005 m2 2.38 (b) 0.01 (b) 0.05 m2 (c) 1.885 m2 (d) 3.77 m2 The maximum usable frequency of an ionospheric layer at 60 incidence and with 8 mHz critical frequency is (a) 16 MHz (b) 16 3 MHz (c) 8 MHz (d) about 6.93 MHz 2.39 ur u r A loop is rotating about the y-axis in a magnetic field E = B0 cos ( t + ) ax T . The voltage in the loop is (a) zero (b) due to rotation only (c) due to transformer action only (d) due to both rotation and transformer action 2.40 The far field of an antenna varies with distance r as (a) 3. 1 r (b) 1 r (c) 2 1 r 3 (d) 1 r Determine the frequency of resonance and the resonant impedance of the parallel circuit shown in Fig.3. What happens when L = CR2? L R C R For more files visit www.educationobserver.com/forum 4. A voltage source of internal impedance Rs + jX s supplies power to a load of impedance RL + jX L in which only RL is variable. Determine the value of RL for maximum power transfer from the source to the load. Also, find the numerical value of RL if the source impedance is 3.0 (purely resistive) and X1 is 4.0 . 5. (a) Draw the transfer characteristic of the circuit of Fig.5, assuming both D1 and D2 to be ideal. (b) How would the characteristic change if D2 is ideal, but D1 is non-ideal in that it has forward resistance of 10 and a reverse resistance of infinity? 1K + + D1 D2 Vi 1K - 1V Vo 2V - 6. Given an irrotational vector field ur u r u r u r F = k1 xy + k2 z 3 ax + 3x 2 k3 Z ay + 3xz 2 y az ( ) ( ) ( ) ur Find V. F at (1,1,-2). SECTION B (50 Marks) Answer any TEN questions. Each question carries 5 marks. 7. The loop transfer function of a single loop control system is given by G (s) H (s) = 100 e sT s (1 + 0.01s ) Using the Nyquist criterion, find the condition for the closed loop system to be stable. 8. The characteristic equation of a feedback control system is s 4 + 20s3 + 15s2 + 2s + K = 0 (i) Determine the range of K for the system to be stable. (ii) Can the system be marginally stable? If so, find the required value of K and the frequency of sustained oscillation. For more files visit www.educationobserver.com/forum 9. Draw a signal flow graph for the following set of algebraic equations: y2 = ay1 gy3 y3 = ey2 + cy 4 y 4 = by2 dy 4 Hence, find the gains 10. y2 y 1 y3 y1 and Consider the system shown in Fig.10. Determine the value of such that the damping ratio is 0.5. Also obtain the values of the rise time tr and maximum overshoot Mp in its step response. R(s) + C(s) 16 s ( s + 0.8 ) - (1+as) 11. Determine the input impedance of the circuit of Fig.11 and investigate if it can be inductive. R2 - C + Z(s) 12. R1 Find the value of R in the circuit of Fig.12 for generating sinusoidal oscillations. Find the frequency of oscillations. R R - C R + R C For more files visit www.educationobserver.com/forum 13. In the circuit of Fig.13, determine the resistance R0 seen by the output terminals. Ignore the effects of R1 and R2. +VCC R1 1K =99 r =1L 5k R2 VS ~ 1K RO +12V 14. The JFET in the circuit of Fig.14 is characterized by the parameters IDSS = 4MA and Vp = 4V . 2k Find (a) V0 if Vi = 0, and (b) Vi if V0 = 0 2k + + Vo - Vi -12V 15. The mod-5 counter shown Q2Q1Q0 = 000, 001, 010, 011 and 100 in Fig.15 counts through states (a) Will the counter lockout if it happen to be in any one of the unused states? (b) Find the maximum rate at which the counter will operate satisfactorily. Assume the propagation delays of flip-flop and AND gate to be tF and t A respectively. J0 1 CLK Q0 K0 Q0 J1 K1 Q1 J2 Q2 Q1 K2 Q2 For more files visit www.educationobserver.com/forum 16. For the TTL circuit shown in Fig.16, find the current through the collector of transistor Q4 when V0 = 0.2V. Assume VCE ( sat ) = 0.2V , = 100 and VBE ( sat ) = 0.7V . The of Q1 in its inverse active mode is 0.01. 5V 500K 20K 40K Q2 A Q4 Q1 VD Q3 12K 17. Write a short assembly language program, without using any arithmetic instruction, to store hexadecimal 5D in the flag register of 8085 microprocessor. Data in other registers of the processor must not alter upon executing this program. 18. Implement a monostable multivibrator using the timer circuit shown in Fig.18. Also determine an expression for ON time T of the output pulse. VCC R Comparator 1 - Threshold + R Comparator 2 2 - Trigger S Q R Output Q + R Discharge GND 19. The pulse rate in a DM system is 56,000 per sec. The input signal is 5 cos(2 1000t) + 2cos(2 2000t) V, with t in sec. Find the minimum value of step size which will avoid slop overload distortion. What will be the disadvantages of choosing a value of larger than the minimum? For more files visit www.educationobserver.com/forum 20. An SSB signal is demodulated by using a synchronous demodulator. However, the locally arranged carrier has a phase error . Determine the effect of the error on demodulation. What will be the effect of this error if the input is DSB-SC in place of SSB? 21. White noise of two-sided spectral density 2 10-6 V2/Hz is applied to a simple R-C low pass filter whose 3dB cut off frequency is 4 kHz. Find the mean squared value of the noise output. 22. T T and t= . Find and 2 2 sketch the pulse obtained by convolving g(t) with itself. The Fourier transform of g(t) is a sine function. Write down to Fourier transform of the pulse obtained by the above convolution. Consider a rectangular pulse g(t) existing between t= 23. A rectangular wave guide with inner dimensions 6 cm 3 cm has been designed for a single mode operation. Find the possible frequency range of operations such that the lowest frequency is 5% above the cut off and the highest frequency is 5% below the cut off of the next higher mode. 24. A plane wave with ur u r j t z ) E = 10e ( ay is incident normally on a thick plane conductor lying in the x-y plane. Its conductivity is 6 106 S/m and surface impedance is 5 10-4 45 . Determine the propagation constant and the skin depth in the conductor. 25. The electric field vector of a wave is given as u r u r u r ur i ( t + 3 x 4y ) 8ax + 6 ay + 5a z V m. E = E0e 125 Its frequency is 10 GHz. (i) Investigate if this wave is a plane wave. (ii) Determine its propagation constant, and (iii) Calculate the phase velocity in y-direction. 26. The region between a pair of parallel perfectly conducting planes of infinite extent in the y- and z directions is partially filled with a dielectric as shown in Fig.26. A 30 GHz TE10 wave is incident on the air dielectric interface as shown. Find the x VSWR at the interface. Air 24cm r=4 5cm

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