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GATE 1999 : 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 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 (a) begh (b) defg (c) adfg 2 1 (d) aegh c 3 b d e f g h 4 1.2 The z-transform F(z) of the function f ( nT ) = anT is (a) 1.3 z T z a (b) z (c) T z+a z T z a (d) z z + a T If f (t ) = F ( s ) , then f (t T ) is equal to (a) esT F ( s ) 1.4 5 (b) e sT F ( s ) (c) F (s) 1+e sT (d) F (s) 1 e sT A 2-port network is shown in Fig.P1.4. the parameter h21 for this network can be given by + R I1 V1 10 F I2 + R R V2 - - (a) 1.5 1 2 (b) + 1 2 (c) 3 2 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 (d) + 3 2 For more files visit www.educationobserver.com/forum 1.6 The first dominant pole encountered in the frequency response of a compensated op-amp is approximately at (a) 5 Hz 1.7 (b) 10 kHz (c) 1 MHz (d) 100 MHz 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(Q1) has a transconductance gm1 , and the common base stage (Q2) has gm2 , then a transconductance the overall transconductance i g= o vi of Q2 io Vo RL Q1 Vi the cascade amplifier is (a) gm1 1.9 (b) gm2 (c) gm1 2 (d) gm2 2 Crossover distortion behaviour is characteristic of (a) Class A output stage (c) Class AB output stage 1.10 (b) Class B output stage (d) Common-base output stage The logical expression y = A + AB is equivalent to (a) y = AB 1.11 (b) y = AB (c) y = A + B (d) y = A + B A Darlington emitter-follower circuit is sometimes used in the output stage of a TTL gate in order to (a) increase its IOL (c) increases its speed of operation 1.12 (b) reduces its IOH (d) reduce power dissipation 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 For more files visit www.educationobserver.com/forum 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 1.14 (b) 1101 (c) 1100 (d) 1110 For a second-order system with the closed-loop transfer function T (s) = 9 2 s + 4s + 9 The settling time for 2-percent band, in seconds, is (a) 1.5 1.15 (c) 3.0 (d) 4.0 The gain margin (in dB) of a system having the loop transfer function G (s) H (s) = (a) 0 1.16 (b) 2.0 2 is s ( s + 1) (b) 3 (c) 6 (d) The system mode described by the state equations 0 1 0 X = x + u 2 3 1 y = 1 1 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 G (s) H (s) = (a) 45 1.18 2 3 is s ( s + 1) (b) -30 (c) 60 (d) 30 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 For more files visit www.educationobserver.com/forum 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 1 6 cos 106 t 1.56 y (t ) = cos 100t 10 100 ( ) ( ( ) ) ( ) The group delay t g and the phase delay t p in seconds, of the channel are (a) t g = 10 6 , t p = 1.56 (b) t g = 1.56, t p = 10 6 (c) t g = 108 , t p = 1.56 10 6 (d) t g = 108 , t p = 1.56 1.20. A modulated signal is given by, s ( t ) = m1 ( t ) cos ( 2 fc t ) + m2 ( t ) sin (2 fc t ) where the baseband signal m1 ( t ) and m2 ( 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 s ( t ) = e at cos ( c + ) t u ( t ) , where a, c and are positive constants, and c . The complex envelope of s(t) is given by (a) exp ( at ) exp j ( c + ) t u (t ) (b) exp ( at ) exp ( j t ) u ( t ) (c) exp j t .u ( t ) (d) exp ( j c + ) t ( ) 1.22. An electric field on a plane is described by its potential V = 20 r 1 + r 2 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) TE110 (b) TE011 (c) TM110 (d) TM111 For more files visit www.educationobserver.com/forum 1.25 Identify which one of the following will NOT satisfy the wave equation. j t 3z ) (a) 50e ( ( 2 (b) sin (10 z + 5t ) (c) cos y + 5t ) (d) sin ( x ) cos ( t ) 2. This question consists of TWENTY-FIVE sub-questions (2.1 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 d (t nT ) is given by s (t ) = 0 n = (a) (c) 2.2. 1 T0 1 T0 exp n = exp n = j2 nt T0 (b) j nt T0 (d) 1 T0 exp n = 1 T0 exp n = j nt T0 j2 nt T0 The Thevenin equivalent voltage VTH appearing between the terminals A and B of the network shown in Fig.P2.2 is given by 3 (a) j16(3-j4) A + (b) j16(3+j4) -j6 j2 100 0 V ~ (c) 16(3+j4) VTH j4 (d) 16(3-j4) B 2.3. The value of R (in ohms) required for maximum power transfer in the network shown in Fig.P2.3 is 5 (a) 2 (b) 4 + (c) 8 4 3A 25V R 20 - (d) 10 2.4. A Delta-connected network with its Wye-equivalent is shown in Fig.P2.4. The resistance R1, R2 and R a 3 (in ohms) are respectively a 5 30 R1 R2 b 15 c b R3 c For more files visit www.educationobserver.com/forum (a) 1.5, 3 and 9 (c) 9, 3 and 1.5 2.5. (b) 3, 9 and 1.5 (d) 3, 1.5 and 9 An n-channel JEFT has IDSS = 2mA and Vp = 4V. Its transconductance gm (in milliohm) for an applied gate-to-source voltage VGS of 2V is: (a) 0.25 2.6. (b) 0.5 (c) 0.75 (d) 1.0 An npn transistor (with C=0.3 pF) has a unity gain cutoff frequency fT of 400 MHz at a dc bias current Ic = 1mA. The value of its C (in pF) is approximately (VT = 26mV ) (a) 15 2.7. (b) 30 (c) 50 An amplifier has an open-loop gain of 100, an input impedance of 1 k , and an output impedance of 100 . A feedback network with a feedback factor of 0.99 is connected to the amplifier in a voltage series feedback mode. The new input and output impedances, respectively, are (a) 10 and 1 (b) 10 and 10 k (c) 100 and 1 2.8. (d) 96 (d) 10k and 1 k A dc power supply has a no-load voltage of 30V, and a full-load voltage of 25 V at a full-load current of 1A. Its output resistance and load regulation, respectively are (a) 5 and 20% (c) 5 and 16.7% 2.9. (b) 25 and 20% (d) 25 and 16.7% An amplifier is assumed to have a single pole high frequency transfer function. The rise time of its output response to a step function input is 35 nsec. The upper 3 dB frequency (in MHz) for the amplifier to a sinusoidal input is approximately at (a) 4.55 (b) 10 (c) 20 (d) 28.6 ( ) 2.10. The minimized form of the logical expression A B C + ABC + ABC + ABC is (a) A C + BC + AB (b) AC + BC + AB (c) AC + BC + AB (d) AC + BC + AB 2.11. For a binary half-sub-tractor having two inputs A and B, the correct set of logical expressions for the outputs D (=A minus B) and X (=borrow) are (a) D = AB + AB, X = AB (b) D = AB + AB + AB, X = AB (c) D = AB + AB, X = AB (d) D = AB + AB, X = AB For more files visit www.educationobserver.com/forum 2.12. The ripple counter shown in Fig.P2.12 works as a Preset J A 1 K Preset Preset Q J Q B Q 1 Q J C K 1 Q K Clock (a) mod 3 up counter (b) mod 5 up counter (c) mod 3 down counter (d) mod 5 down counter 2.13. If CS = A15 A14 A13 is used as the chip select logic of a 4 K RAM in an 8085 system, then its memory range will be (a) 3000 H 3 FFF H (b) 7000 H 7 FFF H (c) 5000 H 5 FFF H and 6000 H 6 FFF H (d) 6000 H 6 FFF H and 7000 H 7 FFF H 2.14. If the closed loop transfer function T(s) of a unity negative feedback system is given by T (s) = n s + a1s an 1s n 1 + an + K + an 1s + an then the steady state error for a unit ramp input is (a) an an 1 (b) an an 2 (c) an 2 an 2 (d) zero 2.15. Consider the points s1 = 3 + j 4 and s2 = 3 j2 in the s-plane. Then, for a system with the open loop transfer function G (s) H (s) = K ( s + 1) 4 (a) s1 is on the root locus, but not s2 (b) s2 is on the root locus, but not s1 (c) both s1 and s2 are on the root locus (d) neither s1 nor s2 is on the root locus For more files visit www.educationobserver.com/forum 2.16. For the system described by the state equation 0 1 0 0 x = 0 0 1 x + 0 u 0.5 1 2 1 If the control signal u is given by u = 0.5 3 5 x + , then the eigen values of the closed-loop system will be (a) 0, -1, -2 (b) 0, -1, -3 (c) -1, -1, -2 2.17. The z-transform of a signal is given by C ( z ) = (a) 2.18. The 1 4 (b) zero Nyquist sampling ( 1z 1 1 z 4 ( 4 1 z 1 2 ) (d) 0, -1, -1 ) . Its final value is (c) 1.0 frequency (in Hz) (d) infinity of a signal given by 6 104 sin c 2 ( 400t ) * 106 sin c 3 (100t ) is (a) 200 (b) 300 (c) 500 (d) 1000 2.19. The peak-to-peak input to an 8-bit PCM coder is 2 volts. The signal power-toquantization noise power ratio (in dB) for an input of 0.5cos ( mt ) is (a) 47.8 (b) 49.8 (c) 95.6 (d) 99.6 2.20. The input to a matched filter is given by 6 10 sin 2 10 t s (t ) = 0 ( ) 0 < 1 < 10 4 sec otherwise The peak amplitude of the filter output is (a) 10 volts (b) 5 volts (c) 10 millivolts (d) 5 millivolts 2.21. Four independent messages have bandwidths of 100 Hz, 200 Hz and 400 Hz, respectively. Each is sampled at the Nyquist rate, and the samples are time division multiplexed (TDM) and transmitted. The transmitted sample rate (in Hz) is (a) 1600 (b) 800 (c) 400 (d) 200 2.22. In a twin-wire transmission line in air, the adjacent voltage maxima are at 12.5 cm and 27.5 cm. The operating frequency is (a) 300 MHz (b) 1 GHz (c) 2 GHz (d) 6.28 GHz For more files visit www.educationobserver.com/forum 2.23. A transmitting antenna radiates 251 W isotropically. A receiving antenna, located 100 m away from the transmitting antenna, has an effective aperture of 500 cm2. The total received by the antenna is (a) 10 W (b) 1 W (c) 20 W (d) 100 W 2.24. In air, a lossless transmission line of length 50 cm with L = 10 H/m, C = 40 pF/m is operated at 25 MHz. Its electrical path length is (a) 0.5 meters (c) 2 (b) meters radians (d) 180 degrees 2.25. A plane wave propagating through a medium r = 8, r = 2, and = 0 has its ur electric field given by E = 0.5 Xe 3 sin 108 t z V m. The wave impedance, in z ( ) ohmsis (a) 377 (b) 198.5 180 (c) 182.9 14 (d) 133.3 SECTION B This section consists of TWENTY questions of FIVE marks each. ANY FIFTEEN out of them have to be answered. If more number of questions are attempted, score off the answers not be evaluated, else, only the first fifteen unscored answers will be considered. 3. In the circuit of Fig.P3, the switch S has remained open for a long time. The switch closes instantaneously at t = 0 (a) Find Vo for t 0 and as t (b) Write an expression for Vo as function of time for 0 t (c) Evaluate Vo at t = 25 sec. 10 12 S + T=0s 25V + - 2.5 F 5 Vo 2A - 4. For the network shown in Fig.P4, evaluate the current I flowing through the 2 resistor using superposition theorem. I 2 10 0 A j8 4 10 20 A For more files visit www.educationobserver.com/forum 5. A coil with a quality factor (Q) of 10 is put in series with a capacitor C1 of 10 F, and the combination is found to draw maximum current when a sinusoidal voltage of frequency 50 Hz is applied. A second capacitor C2 is now in parallel with the circuit. What should be the capacitance of C2 for combined circuit to act purely as a resistance for a sinusoidal excitation at a frequency of 100Hz? Calculate the rms current drawn by the combined circuit at 100 Hz if the applied voltage is 100 V (rms). 6. A bipolar junction transistor amplifier circuit shown in Fig.P6. Assume that the current source Ibias is ideal, and the transistor has vary large b, Vo rb = 0, and r0 . Determined the ac small-signal midband voltage gain V , s input resistance ( Ri ) and output resistance ( Ru ) of the circuit. Assume VT = 26mV VCC Ibias 0.5mA C2= VO RB 100K RL 1K R3 RO 50 C1= ~ Ri 7. VDD A JFET having =50 and rd = 10k is used in a common-source configuration as shown in Fig.P7. The JFET capacitances are C gs = 5pF , C gd = 2 pF , and Cds = 2 pF . Vo Determine the ac small signal midband voltage gain V s frequency of the circuit. 2k 10k RD Vo RS + ~ VS - and the upper 3dB For more files visit www.educationobserver.com/forum 8. Neatly sketch and label the dc transfer characteristic i e V V . ., s. of the circuit ( o in ) R R Vref=1V D1 D2 shown in Fig.P8, as Vin varies from 2V to +2V. Assume ideal op-amp, and the diodes have a forward voltage of 0.6 V and zero incremental resistance. 9. R Vin Vo + A transistor LC oscillator circuit is shown in Fig.P9. Assume that the transistor has very high (so that you may neglect rd ). Derive an equation governing the circuit operation, and find the frequency of oscillation. Also, state the gain condition required for oscillation to start. VCC L C1 C3= VO C2 Ibias RL VEE 10. In the CMOS inverter circuit shown in Fig.P10, the input Vi makes a transition from VOL ( = 0V ) to VOH ( = 5V ) . Determine the high-to-low propagation delay time (t pHL ) when it is driving a capacitive load (CL ) of 20 pF. Device data: NMOS : VTN = 1V ; kN = nCOX VDD=5V W 2 = 40 A / V , = 0, L n W PMOS : VTP = 1V ; k p = pCOX = 20 A / V 2 , = 0. L p VO Vi Neglect body effect. VOH VOL CL 20pF For more files visit www.educationobserver.com/forum 11. The circuit diagram of a synchronous counter is shown in Fig.P.11. Determine the sequence of states of the counter assuming that the initial state is 000 . Give your answer in a tabulor form showing the present state QA ( n) , QB ( n ) , QC ( n) , J K inputs J , K , J , J , K and the next state ( A A B C ) QA ( n +1) , QB ( n +1) , QC ( n +1) . From the table, determine the modulus of the counter. A 1 K Q J Q J B Q 1 K Q J C Q K Q Clock 12. In a certain application, four inputs A, B, C, D (both true and complement forms available) are fed to logic circuit, producing an output F, which operates a relay. The relay turns on when F(ABCD) = 1 for the following states of the inputs (ABCD): 0000 , 0010 , 0101 , 0110 , 1101 and 1110 . States 1000 and 1001 do not occur, and for the remaining states, the relay is off. Minimize F with the help of a Karnaugh map and realize it using a minimum number of 3 input NAND gates. 13. An 8085 assembly language program is given below: MVIC, 03H LXI H, 2000H MOV A, M DRC C LOOP: INX H MOV B, M, CMP B JNC LOOP2 MOV A, B LOOP2: DCR C JNZ LOOP1 STA 2100H HLT For more files visit www.educationobserver.com/forum Contents of the memory locations 2000 H to 2002 H are: 2000 : 18 H 2001:10H, 2002:2 BH. (a) What does the above program do? (b) At the end of the program, what will be (i) the contents of the registers A, B, C, H and L? (ii) the condition of the carry and zero flags? (iii) the contents of the memory locations 2000 H, 2001 H, 2002 H and 2100H. 14. The loop transfer function of a feedback control system is given by G (s) H (s) = K ( s + 1) s (1 + Ts ) (1 + 2s ) ,K > 0 Using Routh-Hurwitz criterion, determine the region of K-T plane in which the closed-loop system is stable. 15. The asymptotic Bode plot of the minimum phase open-loop transfer function G(s) H(s) in as shown in Fig.P15. Obtain the transfer function G(s)H(s) G (s) H (s) -40dB/decade [dB] 20 -20dB/decade 2 0 1 1.0 [rad/s] (log scale) -20 -40dB/decade 16. Consider a feedback system with the open-loop transfer function, given by G (s) H (s) = K s (2s + 1) Examine the stability of the closed loop system using Nyquist stability theory. For more files visit www.educationobserver.com/forum 17. A baseband signal m(t) modulates a carrier to produce the angle modulated signal, Ac cos 2 108 t + k p m ( t ) , where m(t) is shown in Fig.P17. Determine the value of k p so that the peak-to-peak frequency deviation of the carrier is 100 kHz. 12.5 m(t) [Volts] 15 10 5 0 -5 10 5 15 t(ms) -5 -10 18. Input to a linear delta modulator is a sinusoidal signal whose frequency can vary from 200 Hz to 4000 Hz. The input is sampled at eight times the Nyquist rate. The peak amplitude of the sinusoidal signal is 1 volt. (a) Determine the minimum value of the step size in order to avoid slope overload when the input signal frequency is 800 Hz. (b) What is the peak amplitude of the input signal, to just overload the modulator, when the input signal frequency is 200 Hz? (c) Is the modulator overloaded when the input signal frequency is 4000 Hz? 19. The power spectral density (PSD) of a noise process is given by f 108 8 10 1 + 108 SN ( f ) = 0 f < 108 f > 108 The noise is passed through a unit-gain ideal bandpass filter, centered at 50 MHz and having a bandwidth of 2 MHz. (a) Sketch neatly the PSD of the output noise process. (b) Determine the output noise power. (c) Using the band-pass representation for the output noise process, sketch the PSD of the in-phase and quadrature noise components, and determine their respective powers. 20. A plane wave in free space with ur + 11.8y .exp j 4 108 t kz , where x and y are unit vectors in E = 10.0 x ( )( ) ( ) the x-y directions, respectively, is incident normally on a semi-infinite block of ice as shown in Fig.P20. For more files visit www.educationobserver.com/forum For ice, = 0, = 0, and = 9 0 (1 j0.001). (a) Calculate the average power density associated with the incident wave. (b) Calculate the skin depth in ice. (c) Estimate the average power density at a distance of 5 times the skins depth in the ice block, measured from the interface. x , , Incident wave y z o, o Block of ice 21. A 100 m section of an air-filled rectangular wave-guide operating in the TE10 mode has a cross-sectional dimension of 1.071 cm 0.5 cm. Two pulses of 21 GHz and 28 GHz are simultaneously launched at one end of the wave-guide section. What is the time delay difference between the two pulses at the other end of the wave-guide? 22. The average power of an omni directional antenna varies as the magnitude of cos , where is the azimuthal angle. Calculate the maximum Directive Gain of the antenna and the angles at which it occurs.

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