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1 SECTION A (75 marks). This question consists of TWENTYFIVE subquestions (..25) of ONE mark each. For each of these subquestions, 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.. The dependent current source shown in Figure. 5Ω (a) delivers 8 W (b) absorbs 8 W (c) delivers 4 W (d) absorbs 4 W V =2V I 5Ω V A 5.2 In figure.2, the switch was closed for a long time before opening at t =. the voltage Vx at t = is t= (a) 25 V (b) 5 V 2.5A (c) 5 V 2Ω (d) V 5H 2Ω V x.3 Convolution of x(t 5) with impulse function δ(t 7) is equal to (a) x(t 2) (b) x(t 2) (c) x(t 2) (d) x(t 2).4 Which of the following cannot be the Fourier series expansion of a periodic signal? (a) x(t) = 2cos t 3 cos 3t (c) x(t) = cos t.5 (b) x(t) = 2cos πt 7 cos t (d) x(t) = 2cos.5πt sin 3.5 πt.5 In Figure.5, a silicon is carrying a constant current of ma. When the temperature of the diode is 2 C, V D is found to be 7 mv. If the temperature rises to 4 C, V D becomes approximately equal to (a) 74 mv (b) 66 mv (c) 68 mv (d) 7 mv ma V D

2 .6 In a negative feedback amplifier using voltageseries (i.e. voltagesampling series mixing) feedback. (R i and R o denote the input and output resistance respectively) (a) R i decreases and R o decreases (c) R i increases and R o decreases (b) R i decreases and R o increases (d) R i increases and R o increases.7 A 74type opamp has a gainbandwidth product of MHz. A noninverting amplifier using this opamp and having a voltage gain of 2 db will exhibit a 3dB bandwidth of (a) 5 KHz (b) KHz (c) 7 KHz (d) Three identical RCcoupled transistor amplifiers are cascaded. If each of the amplifiers has a frequency response as shown in Figure.8, the overall frequency response is as given in Av db 3 2Hz KHz f Av db Av db (a) 3 4Hz.5KHz 2 f (b) 3 4Hz KHz f (c) Av db (d) Av db 3 3 4Hz 2KHz f Hz.5KHz f.9 4bit 2 s complement representation of a decimal number is. The number is (a) 8 (b) (c) 7 (d) 8

3 . If the input to the digital circuit (Figure.) consisting of a cascade of 2 XORgates is X, then the output Y is equal to Y X (a) (b) (c) X (d) X. The number of comparators required in a 3bit comparator type ADC is (a) 2 (b) 3 (c) 7 (d) 8.2 If the transistor in Figure.2 is in saturation, then C I C I B β dc denotes the dc current gain E (a) I C is always equal to β dc I B (c) I C is greater than or equal to β dc I B (b) I C is always equal to β dc I B (d) I C is less than or equal to β dc I B G s.3 Consider a system with the transfer function ( ) 2 will be.5 when the value of k is s 6 =. Its damping ratio ks s 6 (a) 2 6 (b) 3 (c) 6 (d) 6.4 Which of the following points is NOT on the root locus of a system with the open k loop transfer function G ( s) H ( s) = s s s 3 ( ) ( ) (a) s = j 3 (b) s=.5 (c) s= 3 (d) s =

4 .5 The phase margin of a system with the openloop transfer function ( s) G ( s) H ( s) = is s 2 s ( ) ( ) (a) (b) 63.4 (c) 9 (d).6 The transfer function Y ( s) U ( s) of a system described by the state equations x(t) = 2x(t) 2u(t) and y(t) =.5x(t) is.5 (a) ( s 2 ) (b) ( s 2 ) { }.7 The Fourier transform F e u ( t ) f f (a) eu ( f ) (b) e u ( f ) is equal to.5 (c) ( s 2 ). Therefore, j2πf (d) ( s 2 ) F is j2πt f f (c) eu ( f ) (d) e u ( f ).8 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.9. A MHz sinusoidal carrier is amplitude modulated by a symmetrical square wave of period µsec. Which of the following frequencies will NOT be present in the modulated signal? (a) 99 KHz (b) KHz (c) 2 KHz (d) 3 KHz 5 n= s where x(t) = cos(8π 3 )t and T s =µsec. When y(t) is passed through an ideal lowpass filter with a cutoff frequency of 5KHz, the output of the filter is.2. Consider a sampled signal ( ) 6 y t = x ( t ) δ ( t nt ) (a) 5 6 cos ( 8 3 π ) t (b) 5 ( π 3 ) 5 cos 8 t (c) 5 cos ( π ) t (d) ( π ) cos 8 t.2. For a bitrate of 8 Kbps, the best possible values of the transmitted frequencies in a coherent binary FSK system are (a) 6 KHz and 2 KHz (c) 2 KHz and 4 KHz (b) 2 KHz and 32 KHz (d) 32 KHz and 4 KHz.22. The lineofsight 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

5 (c) at 45 with respect to horizontal polarization (d) at 45 with respect to vertical polarization.23. The VSWR can have any value between (a) and (b) and (c) and (d) and.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.25 The phase velocity for the TE mode in an airfilled rectangular waveguide is (c is the velocity of plane waves in free space) (a) less than c (c) greater than c (b) equal to c (d) none of the above 2. This question consists of TWENTYFIVE subquestions ( ) of TWO marks each. For each of these subquestions, 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. In the network of Figure 2., the maximum power is delivered to R L if its value is I 4Ω.5I 2Ω R L 5V (a) 6Ω (b) 4 3 Ω (c) 6Ω (d) 2Ω

6 2.2. If the 3phase balanced source in Figure 2.2 delivers 5 W at a leading power factor of.844, then the value of Z L (in ohm) is approximately (a) (b) (c) (d) PHASE BALANCED SOURCE 4V Z L Z L Z L X s 2.3. The Laplace transform of a continuoustime signal x(t) is ( ) 2 Fourier transform of this signal exists, then x(t) is 2t t (a) e u ( t ) 2e u ( t ) 2t t (b) e u ( t ) 2e u ( t ) 2t t (c) e u ( t ) 2e u ( t ) 2t t (d) e u ( t ) 2e u ( t ) 5 s =. If the s s If the impulse response of a discretetime system is h n = 5 u n, then the system function H(z) is equal to (a) (c) z z and the system is stable (b) and the system is stable z 5 z 5 z z and the system is unstable (d) and the system is unstable z 5 z 5 n 2.5. An amplifier using an opamp with a slewrate SR = V/µsec has a gain of 4 db. If this amplifier has to faithfully amplify sinusoidal signals from dc to 2 KHz without introducing any slewrate induced distortion, then the input signal level must not exceed. (a) 795 mv (b) 395 mv (c) 79.5 mv (d) 39.5 mv

7 2.6. The circuit in Figure 2.6 employs positive feedback and is intended to generate Vf ( f ) sinusoidal oscillation. If at a frequency fb ( f ) = =, then to sustain V f 6 oscillation at this frequency R 2 ( ) R V f(f) Network B(f) V (f) R (a) R 2 = 5R (b) R 2 = 6R (c) R 2 = 6 R (d) R 2 = A zener diode regulator in Figure 2.7 is to be designed to meet the specifications: I L = ma, V = V and V in varies from 3 V to 5 V. The zener diode has Vz = V and Izk (knee current) = ma. For satisfactory opertion R (a) R 8Ω I L=mA (b) 2Ω R 22Ω I 2 (c) 37Ω R 4Ω (d) R>4Ω V in D z V o R L 2.8. The voltage gain V A = V o i of the JFET amplifier shown in Figure 2.8 is (a) 8 (b) 8 V DD=V I R D=mA D(3KΩ) C 2 v o (c) 6 C (d) 6 v i R G(MΩ) R S(2.5KΩ) C S

8 2.9. The gates G and G 2 in Figure 2.9 have propagation delays of nsec and 2 nsec respectively. If the input V i makes an abrupt change from logic to at time t = t then the output waveform V is G G 2 V V i V i t o V i (a) (b) t t t 2 t 3 t t t 2 t 3 (c) (d) t t t 2 t 3 t t t 2 t The circuit in Figure 2. has two CMOS NOR gates. This circuit functions as a: V SS R V (output) V SS V i C (a) flip flop (c) Monostable multivibrator (b) Schmitt trigger (d) Astable multivibrator

9 2.. Consider the following statements in connection with the CMOS inverter in Figure 2. where both the MOSFETs are of enhancement type and both have a thresh old voltage of 2V. Statement : T conducts when Vi 2V. Statement 2: T is always in saturation when V = V. 5V T 2 V I V T Which of the following is correct? (a) Only Statement is TRUE (c) Both the statements are TRUE (b) Only Statement 2 is TRUE (d) Both the statements are FALSE 2.2. If the input X3, X2, X, X to the ROM in figure 2.2 are 842 BCD numbers, then the outputs YY 3 2 YY are X 3 X 2 X X ROM BCDtoDecimal DECODER D D.. D 8 D 9 X X X X X X X X X X X X X X X X X X X Y 3 Y 2 Y Y (a) gray code numbers (c) excess 3 code numbers (b) 242 BCD numbers (d) none of the above

10 2.3. Consider the following assembly language program. MVI MOV START: JMP MVI XRA OUT HLT B,87H A,B NEXT B,H B NEXT: XRA B JP OUT HLT PORT START PORT2 The execution of the above program in an 885 microprocessor will result in (a) an output of 87H at PORT (b) an output of 87H at PORT2 (c) infinite looping of the program execution with accumulator data remaining at H (d) infinite looping of the program execution with accumulator data alternating between H and 87H 2.4. The system shown in Figure 2.4 remains stable when R(s) k S Y(s) 3 (a) k < (b) < k < (c) < k < 3 (d) k > The transfer function of a system is G ( s) = ( s ) ( s ). For a unit step input to the system the approximate settling time for 2% criterion is (a) sec (b) 4 sec (c) sec (d). sec

11 q s = 2s s 4s 2s 2s The characteristic polynomial of a system is ( ) The system is (a) stable (b) marginally stable (c) unstable (d) oscillatory 2.7. The system with the open loop transfer function G ( s) H ( s) = 2 ( ) s s s gain margin of (a) 6 db (b) db (c) 3.5 db (d) 6 db has a 2.8. An angle modulated signal is given by 6 ( ) = π ( ) s t cos 2 2 t 3 sin5t 4 cos5 t. The maximum frequency and phase deviations of s(t) are (a).5 KHz, 4π rad (b) 6 KHz, 8π rad (c).5 KHz, π rad (d) 7.5 KHz, π rad 2 sin 2πt sin99πt =, = cos 2 and =. The output t t 2.9. In figure 2.9 m ( t ) s ( t ) πt n ( t ) y(t) will be m(t) (a) sin2 π t t s(t) n(t) Lowpass filter Cutoff frequency = Hz (b) sin2 Passband πt sin Gain = s(t) πt cos3πt t t (c) sin2 πt sin.5 πt cos.5πt (d) sin2 πt sin πt cos.75πt t t t t y(t) 2.2. A signal x(t) = cos(24π 3 )t is ideally sampled with a sampling period of 5 µsec and then passed through an ideal lowpass filter with cutoff frequency of 5 KHz. Which of the following frequencies is/are present at the filter output? (a) 2 KHz only (c) 2 KHz and 9 KHz (b) 8 KHz only (d) 2 KHz and 8 KHz 2.2. If the variance 2 of ( ) ( ) ( ) σ x d n = x n x n is onetenth the variance σx of a stationary zero mean discrete time signal x(n), then the normalized Rxx ( k ) autocorrelation function at k = is 2 σ x (a).95 (b).9 (c). (d).5 2

12 ur jπ A plane wave is characterized by.5 ˆ ˆ 2 jωt jkz E = x ye e. This wave is (a) linearly polarized (b) circularly polarized (c) elliptically polarized (d) unpolarized Distilled water at 25 C is characterized by σ =.7 4 mho/m and =78 at a frequency of 3 GHz. Its loss tangent tan δ is ( = 9 /(36π)F/m) (a).3 5 (b).3 3 (c).7 4 /78 (d).7 4 /(78 ) The electric field on the surface of a perfect conductor is 2 V/m. The conductor is immersed in water with =8. The surface charge density on the conductor is ( = 9 /(36π)F/m) (a) C/m 2 (b) 2 C/m 2 (c).8 C/m 2 (d).4 9 C/m A person with a receiver is 5 Km away from the transmitter. What is the distance that this person must move further to detect a 3dB decrease in signal strength? (a) 942 m (b) 27 m (c) 4978 m (d) 532 m SECTION B (75 Marks) This section consists of TWENTY questions (EC3EC22) of FIVE marks each. Attempt ANY FIFTEEN questions. Answers must be given in the answer book provided. Answer for each question must start on a fresh page and must appear at one place only. (Answers to all parts of a question must appear together). 3. The switch in Figure 3 has been in position for a long time and is then moved to position 2 at t =. 25kΩ t= u(t)v I L 2kΩ 5H 6V 2µF V C 4H kω 5kΩ (a) Determine VC ( ) and IL ( ) (b) Determine c ( ) dv t dt at t = (c) Determine V (t) for t >

13 4. For the network shown in Figure 4, R = KΩ, L = 2H, L 2 = 5H, L 3 = H, L 4 = 4H and C =.2 µf. The mutual inductances are M 2 = 3H and M 34 = 2H. Determine (a) the equivalent inductance for the combination of L 3 and L 4. (b) the equivalent inductance across the points A and B in the network. (c) the resonant frequency of the network. I R A L L3 I 2 V s(t) ~ M 2 L 2 M 34 L 4 C B 5. Consider the network in Figure 5. Ω I x 5Ω 2 PORT Ω I 2I 2I x PORT2 I 2 2 (a) Find its shortcircuit admittance parameters. (b) Find the opencircuit impedance Z A triangular voltage waveform V i (t) figure 6(a) is applied at the input to the circuit of Figure 6(b). Assume the diodes to be ideal. V i(t) (a) Determine the output V (t). (b) Neatly sketch the output waveform superimposed on the input V i (t) and label the key points..5kω D 2V t V i(t) D 2 KΩ 7V 5V.5KΩ V (t)

14 7. Figure 7 shows a 2stage amplifier. The transistors Q and Q2 are identical with current gain β = ; further β dc = β ac = β. The Zener diode D z has a break down voltage V z =.7 volt. Assume that D z is in breakdown region and its dynamic resistance r z is zero. The capacitors C and C2 are large and provide negligible impedance at signal frequencies. R 93Ω D Z V Z V EE=V R C2 V CC=V 4KΩ C 2 Q 2 I C R L V C 4KΩ V o V S C R B 93kΩ Q (a) Identify the configuration in each of the amplifier stages (i.e., whether CE, CC, CB etc.) (b) Determine the quiescent quantities I C and V C. V (c) Derive an expression for the voltage gain A V Vs V EE=V and determine its value. (Assume V BE =.7V, r = and Thermal voltage V T = 25 mv) 8. Consider the circuit of Figure 8. The opamp used is ideal. V CC=5V 5V V CC2=2V R KΩ V i Vop R B 5KΩ Q V EE2=2V R F KΩ R L Ω I O V EE=5V

15 (a) In which mode is the BJT operating (i.e. active, saturation or cutoff)? Justify your answer. (b) Obtain an expression relating the output current I and the input voltage V i. (c) Determine I and V P if V i = 2 Volt (V P :output of opamp) (Assume β = 99 and V BE =.7 V) 9. The inputs to a digital circuit shown in Figure 9(a) are the external signals A, B and C. 5V A B C DIGITAL CIRCUIT X D D S Y Table 9 S Y D D ( AB, and C are not available). The 5V power supply (logic ) and the ground (logic ) are also available. The output of the circuit is X = AB ABC. (a) Write down the output function in its canonical SOP and POS forms. (b) Implement the circuit using only two 2: multiplexers shown in Figure 9(b), where S is the dataselect line, D and D are the input data lines and Y is the output lines. The function table for the multiplexer is given in table 9.. Each transistor in Figure has dc current gain β dc = 5, cutin voltage Vγ =.65V and V BE, sat =.75 V. The output voltage V for T 2 in saturation can be as high as.2 V. Assume.7 V drop across a conducting pn junction. Determine? R C2=kΩ R B V o(output) V i(input) T I B2 T 2 R b=5kω 2V

16 (a) the minimum value I B2 necessary to keep T 2 saturation. (b) the maximum permissible value for the resistance R B. (c) the worstcase high input (logic ) and the worstcase low input (logic ) for which T 2 will be either in saturation or in cut off.. It is required to design a binary mod5 synchronous counter using AB flipflops such that the output Q 2 Q Q changes as.. and so on. The excitation table for the AB flipflop is given in table. (a) Write down the state table for the mod5 counter. (b) Obtain simplified SOP expressions for the inputs A 2, B 2, A, B, A and B in terms of Q 2, Q, Q and their complements. (c) Hence, complete the circuit diagram for the mod5 counter given in Figure using minimum number of 2input NANDgate only. A B Q n Q n Q n A 2 Q 2 A Q A Q B 2 Q 2 B Q B Q Clock 2. An 885 microprocessor operating at 5 MHz clock frequency execute the following routine. START MOVE A,B OUT DCR STA JMP 55H B FFF8H START (a) Determine the total number of machine cycles required to execute this routine till the JMP instruction is executed for the first time. (b) Determine the time interval between two consecutive MEMW signals.

17 (c) If the external logic controls the READY line so that three WAIT states are introduced in the I/O WRITE machine cycle, determine the time interval between two consecutive MEMW signals. 3. A unity feedback system has the plant transfer function G ( s) (a) Determine the frequency at which the plant has a phase lag of 9 (b) An integral controller with transfer function G ( s) p = ( s ) ( 2s ) k c = is placed in the feedforward path of the feedback system. Find the value of k such that the s compensated system has an openloop gain margin of 2.5. (c) Determine the steady state errors of the compensated system to unitstep and unitramp inputs. 4. The Nyquist plot of an allpole second order openloop system is shown in Figure 4. Obtain the transfer function of the system. Imag ω=.5 ω= Real 2.5 ω= The block diagram of a linear time invariant system is given in Figure 5. U(s) X 2(s) Σ /s Σ /s X (s) Σ Y(s) 2

18 (a) Write down the state variable equations for the system in matrix form T 2. assuming the state vector to be x ( t ) x ( t ) (b) Find out the state transition matrix. (c) Determine y(t), t, when the initial values of the state at time t = are x () =, and x 2 () =. 6. A deterministic signal x(t) = cos2πt is passed through a differentiator as shown in Figure 6. x(t) d 2π dt y(t) (a) Determine the autocorrelation R xx (T) and the power spectral density S xx (f). (b) Find the output power spectral density S yy (f). (c) Evaluate R xy () and R xy A DSBSC modulated signal s(t) = cos (2π 6 tφ)m(t ) is corrupted by an additive white Gaussian noise of power spectral density 4 W/Hz. The message power spectral density S mm (f) is as shown in Figure 7 and φ is uniformly distributed over the range to 2π. S mm(f) 3 W/Hz f 3KHz 3KHz (a) Express the signal autocorrelation function R SS (T) in terms of the message autocorrelation function R mm (T). Clearly state the necessary assumptions. (b) Determine the signal power spectral density S SS (f). (c) Find the power of the modulated signal and the noise power in the transmissions bandwidth. 8. A continuous time signal with finite energy, band limited from 3 MHz to 5 MHz is ideally sampled, encoded by a fixed length PCM coder and then transmitted over a digital channel of capacity 7 Mbps. The probability density function (pdf) at the output of the sampler is uniform over the range 2V to 2V. (a) Determine the minimum sampling rate necessary for perfect reconstruction. (b) Determine the maximum SNR (in db) that may be achieved.

19 9. A discrete memoryless source generates either or at a rate of 6 Kbps; is generated three times more frequently than. A coherent binary PSK modulator is employed to transmit these bits over a noisy channel. The received bits are detected in a correlator fed with the basis function of unit energy (for this binary PSK scheme) as the reference signal. The receiver makes a decision in favour of if the correlator output is positive, else decides in favour of. If and are represented as ( 6 2 cos64π 3 t ) V and ( 6 2 cos64π 3 ) then t V respectively, (a) determine the transmitted signal energy per bit. (b) determine the basis function of unit energy for this binary PSK scheme. (c) determine the probability that the receiver makes a decision in favour of when the channel noise is characterized as zeromean AWGN with power N 4 spectral density = 3.25 W / Hz 2 2. Transmission line transformation of a load Z L and Z is given by Z jz L Z = Z Z jz L tan tan ( βl ) ( β l ) (a) Show that the above transformation implies that the impedance Z gets * transformed to ZL for real Z. (b) What is the importance of the result derived in (a)? 2. Consider a parallel plate waveguide with plate separation d as shown in Figure 2 electric and magnetic fields for the TEMmode are given by E = Ee H x y E = e n jkz jωt jkz jωt where k = ηωε (a) Determine the surface charge densities p s on the plates at x = and x = d. (b) Determine the surface current densities J r s on the same plates. (c) Prove that p s and J r s satisfy the current continuity condition. x d z

20 22. Consider a linear array of two halfwave dipoles A and B as shown in Figure 22. The dipoles are 4 λ apart and are excited in such a way that the current on element B legs that on element A by 9 in phase. (a) Obtain the expression for the radiation pattern for E in the XY plane (i.e, θ=9 ) (b) Sketch the radiation pattern obtained in (a). A B Y λ/4 φ= X

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Join discussion of this test paper at SECTION A (75 marks). This question consists of TWENTYFIVE subquestions (..25) of ONE mark each. For each of these subquestions, four possible alternatives (A,B, C and D) are given, out of which ONLY ONE