GATE EC Q.1 - Q.20 carry one mark each. G are nonzero, and one of its. p11

Transcription

1 GATE EC 8 Q. - Q. carry one mark each. p p MCQ. All the four entrie of the # matri p p G are nonzero, and one of it eigenvalue i zero. hich of the following tatement i true? (A) pp pp (B) pp pp OL. (C) pp pp (D) pp + pp The product of Eigen value i equal to the determinant of the matri. ince one of the Eigen value i zero, the product of Eigen value i zero, thu determinant of the matri i zero. Thu pp pp Hence (C) i correct anwer. MCQ. The ytem of linear equation 4+ y 7 + y 6 ha (A) a unique olution (C) an infinite number of olution (B) no olution (D) eactly two ditinct olution OL. The given ytem i 4 7 G y G 6 G e have and Now 4 A G A C 4 Rank of matri ρ( A) < G Rank of matri ρ ( C ) ince ρ( A)! ρ ( C) there i no olution. Hence (B) i correct anwer. MCQ. The equation in() z ha

2 Page GATE EC 8 (A) no real or comple olution (B) eactly two ditinct comple olution (C) a unique olution (D) an infinite number of comple olution OL. in z can have value between to +. Thu no olution. Hence (A) i correct olution. MCQ.4 OL.4 MCQ.5 For real value of, the minimum value of the function f () ep() + ep( ) i (A) (B) (C).5 (D) Hence (A) i correct anwer. e have f () e + e For >, e > and < e < For <, < e < and e > Thu f () have minimum value at and that i e + e. hich of the following function would have only odd power of in it Taylor erie epanion about the point? (A) in( ) (B) in( ) (C) co( ) (D) co( ) OL.5 MCQ.6 OL.6 Hence (A) i correct anwer. 5 in ! 5! co ! 4! Thu only in( ) will have odd power of. hich of the following i a olution to the differential equation (A) t () (C) t () e - t (B) t () t (D) t () Hence (B) i correct anwer. d() t e have + () t dt e -t t d() t + t ()? dt or ( D+ ) ( t) ince m, t () Ce Thu only (B) may be olution. MCQ.7 In the following graph, the number of tree ( P ) and the number of cut-et ( Q ) are

3 Page GATE EC 8 (A) P, Q (B) P, Q 6 (C) P 4, Q 6 (D) P 4, Q OL.7 The given graph i There can be four poible tree of thi graph which are a follow: There can be 6 different poible cut-et. Hence (C) i correct option. MCQ.8 In the following circuit, the witch i cloed at t. The rate of change of current di ( + ) i given by dt (A) (B) RI L (C) ( R+ R ) I (D) L OL.8 Initially i ( ) therefore due to inductor i ( + ). Thu all current I will flow in reitor R and voltage acro reitor will be I R. The voltage acro inductor will be equal to voltage acro R a no current flow through R.

4 Page 4 GATE EC Thu vl ( ) IR but + + di( ) vl ( ) L dt Thu di( + + ) v ( ) dt L IR L L Hence (B) i correct option. MCQ.9 OL.9 The input and output of a continuou time ytem are repectively denoted by t () and yt. () hich of the following decription correpond to a caual ytem? (A) yt ( ) t ( ) + t ( + 4) (B) yt ( ) ( t 4) t ( + ) (C) yt ( ) ( t+ 4) t ( ) (D) yt ( ) ( t+ 5) t ( + 5) The output of caual ytem depend only on preent and pat tate only. In option (A) y() depend on ( ) and () 4. In option (B) y() depend on (). In option (C) y() depend on ( ). In option (D) y() depend on () 5. Thu only in option (C) the value of yt () at t depend on ( ) pat value. In all other option preent value depend on future value. Hence (C) i correct anwer MCQ. The impule repone ht () of a linear time invariant continuou time ytem i decribed by ht () ep( αtut ) () + ep( βtu ) ( t) where u( t) denote the unit tep function, and α and β are real contant. Thi ytem i table if (A) α i poitive and β i poitive (B) α i negative and β i negative (C) α i negative and β i negative (D) α i negative and β i poitive OL. MCQ. Hence (D) i correct anwer. αt βt e have ht () e u() t + e u( t) Thi ytem i table only when bounded input ha bounded output For tability α t < for t > that implie α < and β t > for t > that implie β >. Thu, α i negative and β i poitive. The pole-zero given below correpond to a

5 Page 5 GATE EC 8 (A) Law pa filter (C) Band filter (B) High pa filter (D) Notch filter OL. Percent overhoot depend only on damping ratio, ξ. ξπ ξ M p e If M p i ame then ξ i alo ame and we get ξ co θ Thu θ contant The option (C) only have ame angle. Hence (C) i correct option. MCQ. tep repone of a et of three econd-order underdamped ytem all have the ame percentage overhoot. hich of the following diagram repreent the pole of the three ytem? OL. Tranfer function for the given pole zero plot i: ( + Z)( + Z) ( + P)( + P) From the plot Re (P and P )>(Z and Z ) o, thee are two lead compenator. Hence both high pa filter and the ytem i high pa filter.

6 Page 6 GATE EC 8 Hence (C) i correct option. MCQ. hich of the following i NOT aociated with a p n junction? (A) Junction Capacitance (B) Charge torage Capacitance (C) Depletion Capacitance (D) Channel Length Modulation OL. Channel length modulation i not aociated with a p n junction. It i being aociated with MOFET in which effective channel length decreae, producing the phenomenon called channel length modulation. Hence option (D) i correct. MCQ.4 OL.4 MCQ.5 hich of the following i true? (A) A ilicon wafer heavily doped with boron i a p + ubtrate (B) A ilicon wafer lightly doped with boron i a p + ubtrate (C) A ilicon wafer heavily doped with arenic i a p + ubtrate (D) A ilicon wafer lightly doped with arenic i a p + ubtrate Trivalent impuritie are ued for making p type emiconductor. o, ilicon wafer heavily doped with boron i a p + ubtrate. Hence option (A) i correct For a Hertz dipole antenna, the half power beam width (HPB) in the E -plane i (A) 6c (B) 8c (C) 9c (D) 45c OL.5 The beam-width of Hertizian dipole i 8c and it half power beam-width i 9c. Hence (C) i correct option MCQ.6 OL.6 For tatic electric and magnetic field in an inhomogeneou ource-free medium, which of the following repreent the correct form of Mawell equation? (A) 4$ E, 4# B (B) 4$ E, 4$ B (C) 4# E, 4# B (D) 4# E, 4$ B Mawell equation 4 B 4$ E ρ/e 4# E B 4# H t D+ J For tatic electric magnetic field 4$ B 4$ E ρ/e 4# E 4# H J Hence (D) i correct option

7 Page 7 GATE EC 8 MCQ.7 In the following limiter circuit, an input voltage Vi in πt i applied. Aume that the diode drop i.7 V when it i forward biaed. hen it i forward biaed. The zener breakdown voltage i 6.8 V The maimum and minimum value of the output voltage repectively are (A) 6. V,.7 V (B).7 V, 7.5 V (C) 7.5 V,.7 V (D) 7.5 V, 7.5 V OL.7 MCQ.8 OL.8 For the poitive half of V i, the diode D i forward bia, D i revere bia and the zener diode i in breakdown tate becaue Vi > 68.. Thu output voltage i V V For the negative half of VD i, i forward bia thu Then V 7. V Hence (C) i correct option A ilicon wafer ha nm of oide on it and i furnace at a temperature above c C for further oidation in dry oygen. The oidation rate (A) i independent of current oide thickne and temperature (B) i independent of current oide thickne but depend on temperature (C) low down a the oide grow (D) i zero a the eiting oide prevent further oidation Oidation rate i zero becaue the eiting oide prevent the further oidation. Hence option (D) i correct. MCQ.9 The drain current of MOFET in aturation i given by I K( V V ) where K i a contant. The magnitude of the tranconductance g m i D G T OL.9 (A) KV ( V) V G T D (B) KV ( V) G T (C) Id KV ( V) (D) V G V D VG Hence option (B) i correct. g ID m ( ) V V KV G V T KV ( G VT ) G G G T

8 Page 8 GATE EC 8 MCQ. Conider the amplitude modulated (AM) ignalacco ωct+ co ωmtco ωct. For demodulating the ignal uing envelope detector, the minimum value of A c hould be (A) (B) (C).5 (D) OL. Hence (A) i correct option e have AM () t Acco ωc+ co ωmtco ωct A C c + A c co ω m tmco ωct For demodulation by envelope demodulator modulation inde mut be le than or equal to. Thu # Ac A c $ Hence minimum value of Ac Q. to Q.75 carry two mark each MCQ. The Thevenin equivalent impedance Z th between the node P and Q in the following circuit i OL. (A) (B) + + (C) + + (D) Killing all current ource and voltage ource we have, Z th ( + ) ( + ) ( + )( + ) [ ] ( + ) + ( + ) + + +

9 Page 9 GATE EC 8 or Z th Alternative : Here at DC ource capacitor act a open circuit and inductor act a hort circuit. Thu we can directly calculate thevenin Impedance a Ω Hence (A) i correct option. MCQ. The driving point impedance of the following network i given by Z () The component value are (A) L 5 H, R.5 Ω, C. F (B) L. H, R.5 Ω, C 5F (C) L 5 H, R Ω, C.F (D) L. H, R Ω, C 5F OL. MCQ. Hence (D) i correct option. Z () R C L C + RC + e have been given Z () Comparing with given we get. or C 5 F C. or R Ω RC or L. H LC LC The circuit hown in the figure i ued to charge the capacitor C alternately from two current ource a indicated. The witche and are mechanically coupled and connected a follow: For nt # t # ( n + ) T, ( n,,,..) to P and to P For ( n+ ) T # t # ( n+ ) T, ( n,,,...) to Q and to Q

10 Page GATE EC 8 OL. Aume that the capacitor ha zero initial charge. Given that ut () i a unit tep function, the voltage vc () t acro the capacitor i given by / (A) ( ) n tu( t nt) n / (B) ut () + ( ) n ut ( nt) n / (C) tu( t) + ( ) n u( t nt)( t nt) n ( t nt) ( t nt) (D) / 65. e + 5. e T@ n Voltage acro capacitor i t V c # C idt Here C F and i A. Therefore t V c # dt For < t < T, capacitor will be charged from V # V c dt t t At t T, Vc T Volt For T < t < T, capacitor will be dicharged from T volt a # V c T dt T t T t At t T, V c volt For T < t < T, capacitor will be charged from V # t V c dt t T T At t T, Vc T Volt For T < t < 4T, capacitor will be dicharged from T Volt # V c T dt 4T t t T At t 4 T, V c Volt For 4T < t < 5T, capacitor will be charged from V t # V c dt t 4T 4T

11 Page GATE EC 8 At t 5 T, Vc T Volt Thu the output waveform i Only option C atify thi waveform. Hence (C) i correct option. MCQ.4 The probability denity function (pdf) of random variable i a hown below The correponding commutative ditribution function CDF ha the form OL.4 CDF i the integration of PDF. Plot in option (A) i the integration of plot given in quetion. Hence (A) i correct option. MCQ.5 The recurion relation to olve e - uing Newton - Raphon method i n n (A) e (B) e OL.5 n+ n (C) ( ) e n+ + n (D) n + e Hence (C) i correct anwer. e have e - or f () e - f'( ) + e - n+ n n n e ( n) n e n+ n

12 Page GATE EC 8 The Newton-Raphon iterative formula i f ( n) n + n f'( ) Now f ( n ) n e - n f'( n ) + e - n - n Thu n + n e n ( + n) e n + - -n e + e MCQ.6 The reidue of the function fz () (A) (C) 6 n - (B) n at z i ( z + ) ( z ) 6 (D) OL.6 Hence (A) i correct anwer. n - Re fz () d n z a ( z a) f( z) ( n )! n - dz Here we have n and a z a Thu Re fz () z d ( z ) ( )! dz ; ( z ) ( z ) + E z d dz ; ( z + ) E ; z a ( z + ) E z a 64 a MCQ.7 Conider the matri P G. The value of e p i e e e e e + e e e (A) > H (B) > H e e 5e e e 4e e + e 5e e e e e e e e (C) > H (D) > H e 6e 4e + 6 e + e e + e OL.7 Hence (D) i correct anwer. e P - - L 6 ( I - L e G L e + G ( + )( + ) - - o Go ( + )( + ) - - ( )( ) ( )( ) L - f> + + Hp e e e e G e + e e + e

13 Page GATE EC 8 MCQ.8 In the Taylor erie epanion of ep() + in() about the point π, the coefficient of ( π) i (A) ep( π ) (B) 5. ep( π) (C) ep( π ) + (D) ep( π) OL.8 Taylor erie i given a ( ) f () fa ( ) a a + f '( a ) + f "( a ) +...!! For π we have ( ) Thu f () f( ) π + π f'( π) + π f"( )...!! Now f () e + in f'( ) e + co f"( ) e in π π f"( π ) e in π e f"( π) Thu the coefficient of ( π) i! Hence (B) i correct anwer. MCQ.9 P () Mep_ i Nep_ i i the probability denity function for the real random variable X, over the entire ai, M and N are both poitive real number. The equation relating M and N i (A) M N (B) M+ N (C) M+ N (D) M+ N OL.9 Correct Option i ( ) 4 MCQ. The value of the integral of the function gy (,) 4+ y along the traight line egment from the point (,) to the point (,) in the y plane i (A) (B) 5 (C) 4 (D) 56 OL. The equation of traight line from (,) to (,) i y. Now 4 gy (,) 4 + y or, 4 g (, ) Now # g (, ) # ( ) d [ + ] Hence (A) i correct anwer. 4 5 MCQ. A linear, time - invariant, caual continuou time ytem ha a rational tranfer function with imple pole at and 4 and one imple zero at.

14 Page 4 GATE EC 8 OL. A unit tep ut () i applied at the input of the ytem. At teady tate, the output ha contant value of. The impule repone of thi ytem i (A) [ ep( t) + ep( 4t)] u( t) (B) [ 4 ep( t) ep( 4t) ep( t)] u( t) (C) [ 4 ep( t) + ep( 4t)] u( t) (D) [ 5. ep( t) + 5. ep( 4t)] u( t) Hence (C) i correct anwer. K ( + ) G (), and R () ( + )( + 4) K ( + ) C () GR () () ( + )( + 4) K + K K 8 4( + ) 8( + 4) Thu ct () K e e u() t 8 4 t 8 : + 4t D At teady-tate, c( ) Thu K or K 8 8 Then, G () 8( + ) ( + )( + 4) 4 ( + 4) ( + ) ht () L G() ( 4e t 4t + e ) u( t) MCQ. The ignal t () i decribed by for # t # + t () ) otherwie Two of the angular frequencie at which it Fourier tranform become zero are (A) π,π (B).5 π,.5π (C), π (D) π,.5π OL. Hence (A) i correct anwer. for # t # + e have t () ) otherwie Fourier tranform i e j ω t jωt () t dt e dt # # j t [ e ] ω jω jω jω ( e e ) ( j in ω) jω jω in ω ω Thi i zero at ω π and ω π

15 Page 5 GATE EC 8 MCQ. A dicrete time linear hift - invariant ytem ha an impule repone hn [ ] with h[ ], h[ ], h[ ], and zero otherwie The ytem i given an input equence n [ ] with [ ] [ ], and zero otherwie. The number of nonzero ample in the output equence yn, [ ] and the value of y[ ] are repectively (A) 5, (B) 6, (C) 6, (D) 5, OL. Hence (D) i correct anwer. Given hn ( ) [,, ] n ( ) [,, ] yn ( ) n ( )* hn ( ) The length of yn [ ] i L+ L + 5 / k yn ( ) n ( )* hn ( ) khn ( ) ( k) / k y() kh () ( k) ( ) h( ) + ( ) h( ) + ( ) h( ) h() + + h() + There are 5 non zero ample in output equence and the value of y[ ] i. MCQ.4 Conider point P and Q in the y plane, with P (,) and Q (,). The Q line integral # ( d + ydy) along the emicircle with the line egment PQ a it P diameter (A) i (B) i (C) i (D) depend on the direction (clockwie or anit-clockwie) of the emicircle OL.4 Hence (B) i correct anwer. # I ( d + ydy) P Q Q Q # d + # ydy P # d + ydy # P MCQ.5 Let t () be the input and yt () be the output of a continuou time ytem. Match the ytem propertie P, P and P with ytem relation R, R, R, R4 Propertie Relation P : Linear but NOT time - invariant R : yt () tt () P : Time - invariant but NOT linear R : yt () tt ()

16 Page 6 GATE EC 8 P : Linear and time - invariant R : yt () t () R4 : yt () t ( 5) (A) (P, R), (P, R), (P, R4) (B) (P, R), (P, R), (P, R4) (C) (P, R), (P, R), (P, R) (D) (P, R), (P, R), (P, R) OL.5 Mode function are not linear. Thu yt () t () i not linear but thi function i time invariant. Option (A) and (B) may be correct. The yt () tt () i not linear, thu option (B) i wrong and (a) i correct. e can ee that R: y( t) t ( t) Linear and time variant. R : y( t) t ( t) Non linear and time variant. R : y( t) ( t) Non linear and time invariant R4 : y( t) ( t 5) Linear and time invariant Hence (B) i correct anwer. MCQ.6 OL.6 A memory le ource emit n ymbol each with a probability p. The entropy of the ource a a function of n (A) increae a log n (B) decreae a log( n ) (C) increae a n The entropy i m H p log / i bit p i i ince p p... p n n n H / log n log n n i Hence (A) i correct option. (D) increae a nlog n MCQ.7 { n ( )} i a real - valued periodic equence with a period N. n ( ) and Xk () form N-point Dicrete Fourier Tranform (DFT) pair. The DFT Yk () of the equence N yn ( ) rn ( ) ( + r) N / i r (A) Xk () N (B) XrXk () ( + r) N N (C) XrXk () ( + r) N / (D) r / r OL.7 Hence (A) i correct anwer. N - / r Given : yn ( ) rn () ( + r) N

17 Page 7 GATE EC 8 It i Auto correlation. Hence yn ( ) r ( n) X( k) DFT MCQ.8 Group I lit a et of four tranfer function. Group II give a lit of poible tep repone yt. () Match the tep repone with the correponding tranfer function. (A) P, Q, R 4, (B) P, Q, R 4, (C) P, Q, R 4, (D) P, Q 4, R, OL.8 Hence (D) i correct option. P 5 ξω n, ξ " Undamped Graph + 5 Q 6 ξω, > n ξ " Overdamped Graph 4 R 6 ξω, n ξ " Critically Graph 7 ξω n 7, ξ < " underdamped Graph MCQ.9 A certain ytem ha tranfer function G () α 4

18 Page 8 GATE EC 8 where α i a parameter. Conider the tandard negative unity feedback configuration a hown below hich of the following tatement i true? (A) The cloed loop ytem i never table for any value of α (B) For ome poitive value of α, the cloed loop ytem i table, but not for all poitive value. (C) For all poitive value of α, the cloed loop ytem i table. (D) The cloed loop ytem table for all value of α, both poitive and negative. OL.9 Hence (C) i correct option. The characteritic equation of cloed lop tranfer function i () () GH α or 4 8 α or ( ) 4 α Thi will be table if ( ) > > " α α +. Thu ytem i table for all poitive value of α. MCQ.4 A ignal flow graph of a ytem i given below The et of equalitie that correpond to thi ignal flow graph i (A) dt d u u β γ α γ α β + J L K K K J L K K K e N P O O O N P O O O o R T R T V X V X (B) dt d u u α α β γ γ β + J L K K K J L K K K e N P O O O N P O O O o R T R T V X V X (C) dt d u u α β α β γ γ + J L K K K J L K K K e N P O O O N P O O O o R T R T V X V X

19 Page 9 GATE EC 8 J (D) d N R V α β J N R V K O K O u dt K O γ α K O+ e u o K O β α K O L P T XL P T X OL.4 e labeled the given FG a below : From thi FG we have o γ+ β+ μ o γ+ α o β α+ u R V R VR V R V γ β u Thu γ α + e u o β α T X T XT X T X Hence (C) i correct option. MCQ.4 OL.4 The number of open right half plane of G () i (A) (B) (C) (D) The characteritic equation i + G () 5 4 or ubtituting z we have 5 4 z + 5z + 6z + z + z+ The routh table i hown below. A there are tow ign change in firt column, there are two RH pole. z 5 6 z 4 5 z z 4 z 7 4 z

20 Page GATE EC 8 Hence (C) i correct option. MCQ.4 OL.4 MCQ.4 The magnitude of frequency repone of an underdamped econd order ytem i 5 at rad/ec and peak to at 5 rad/ec. The tranfer function of the ytem i (A) 5 (B) (C) (D) For underdamped econd order ytem the tranfer function i T () K n ω + ξωn + ωn It peak at reonant frequency. Therefore Reonant frequency ω r ωn ξ and peak at thi frequency μ r 5 ξ ξ e have ω r 5, and μ r. Only option (A) atify thee value. ω n, ξ where ω r ` 5 4 j and μ r 5 Hence (C) i correct option. 4 Hence atified Group I give two poible choice for the impedance Z in the diagram. The circuit element in Z atify the condition RC> RC. The tranfer function V V i repreent a kind of controller. Match the impedance in Group I with the type of controller in Group II

21 Page GATE EC 8 (A) Q, R (B) Q, R (C) Q, R (D) Q, R OL.4 The given circuit i a inverting amplifier and tranfer function i Vo Z ZCR ( ) + V R i R CR+ ( CR+ ) For Q, Z C Vo ( CR+ ) ( CR+ ) # Vi C R For R, Z R ( CR+ ) Vo R ( CR+ ) # V ( C R + ) R i ince RC> RC, it i lag compenator. Hence (B) i correct option. PID Controller MCQ.44 For the circuit hown in the following figure, tranitor M and M are identical NMO tranitor. Aume the M i in aturation and the output i unloaded. OL.44 The current I i related to I bia a (A) I Ibia + I (B) I Ibia (C) I I V Vout bia c DD R m E (D) I I I By Current mirror, ^ L h I Ibia ^ h L bia

22 Page GATE EC 8 ince MOFET are identical, Thu b L l b L l Hence I I bia Hence (B) i correct option. MCQ.45 The meaured tran conductance g m of an NMO tranitor operating in the linear region i plotted againt the gate voltage V G at a contant drain voltage V D. hich of the following figure repreent the epected dependence of g m on V G? OL.45 Hence option (C) i correct. A V D contant Thu g m \ ( V V ) hich i traight line. G T MCQ.46 Conider the following circuit uing an ideal OPAMP. The I-V characteritic of the V diode i decribed by the relation I I_ evt i where VT 5 mv, I μa and V i the voltage acro the diode (taken a poitive for forward bia). For an input voltage V i V, the output voltage V i (A) V (C).7 V (B). V (D). V OL.46 The circuit i uing ideal OPAMP. The non inverting terminal of OPAMP i at ground, thu inverting terminal i alo at virtual ground.

23 Page GATE EC 8 MCQ.47 Thu current will flow from -ive terminal ( Volt) to - Volt ource. Thu the current I i ( ) I k k The current through diode i V I I_ evt i Now VT 5 mv and I μa 6 V Thu I e 8 5# B or V 6. V Now V I# 4k + V # 4k V k Hence (B) i correct option. The OPAMP circuit hown above repreent a 5 (A) high pa filter (C) band pa filter (B) low pa filter (D) band reject filter OL.47 The circuit i uing ideal OPAMP. The non inverting terminal of OPAMP i at ground, thu inverting terminal i alo at virtual ground.

24 Page 4 GATE EC 8 Thu we can write or R v i + L v v i v R R C + R ( R + L)( R C + ) and from thi equation it may be eaily een that thi i the tandard form of T.F. of low pa filter H () K ( R + L)( R C + ) and form thi equation it may be eaily een that thi i the tandard form of T.F. of low pa filter H () K a + b + b Hence (B) i correct option. MCQ.48 Two identical NMO tranitor M and M are connected a hown below. V bia i choen o that both tranitor are in aturation. The equivalent g m of the pair i defied to be Iout at contant V V out The equivalent g m of the pair i i (A) the um of individual g m ' of the tranitor (B) the product of individual g m of the tranitor (C) nearly equal to the g m of M (D) nearly equal to g g m of M OL.48 The current in both tranitor are equal. Thu g m i decide by M. Hence (C) i correct option. MCQ.49 An 885 eecute the following intruction 7 LXI H, A H 7 DAD H 44 PCHL All addre and contant are in He. Let PC be the content of the program counter and HL be the content of the HL regiter pair jut after eecuting PCHL. hich of the following tatement i correct? (A) PC 75H (B) PC AH HL AH HL 75H

25 Page 5 GATE EC 8 (C) PC 64H HL 64H (D) PC 64H HL 75H OL.49 7H LXI H, AH ; Load 6 bit data A in HL pair 7H DAD H ; 64H " HL 74H PCHL ; Copy the content 64H of HL in PC Thu after eecution above intruction contet of PC and HL are ame and that i 64H Hence (C) i correct anwer. MCQ.5 An atable multivibrator circuit uing IC 555 timer i hown below. Aume that the circuit i ocillating teadily. The voltage V c acro the capacitor varie between (A) V to 5 V (B) V to 6 V (C).6 V to 6 V (D).6 V to 5 V OL.5 Correct Option i ( ) MCQ.5 ilicon i doped with boron to a concentration of 4# 7 atom cm. Aume the intrinic carrier concentration of ilicon to be 5. # / cm and the value of kt/ q to be 5 mv at K. Compared to undopped ilicon, the fermi level of doped ilicon (A) goe down by. ev (B) goe up by. ev (C) goe down by.47 ev (D) goe up by.47 ev OL.5 Hence option (C) i correct. E E kt ln NA n i N A 4# 7

26 Page 6 GATE EC 8 n i 5. # 7 E E 5 e ln 4 # #. 47 ev 5. # Hence fermi level goe down by.47 ev a ilicon i doped with boron. MCQ.5 The cro ection of a JFET i hown in the following figure. Let V c be V and let V P be the initial pinch -off voltage. If the width i doubled (with other geometrical parameter and doping level remaining the ame), then the ratio between the mutual tran conductance of the initial and the modified JFET i (A) 4 (B) (C) / Vp e o (D) / V p / Vp e / V p ( Vp ) [ ( V )] p o OL.5 MCQ.5 Hence option (C) i correct Pinch off voltage V e N D P ε Let V P V P Now VP VP ( ) or 4V P V P Initial tranconductance g m K Vbi VG n ; V E For firt condition For econd condition g m g m ( ) Kn Kn V G ; p V E P P ( ) Kn K V G ; Dividing gm / VP g f p m /( VP) Hence V P V P Conider the chmidt trigger circuit hown below A triangular wave which goe from - to V i applied to the inverting input of P 4V P E

27 Page 7 GATE EC 8 OPMAP. Aume that the output of the OPAMP wing from +5 V to -5 V. The voltage at the non-inverting input witche between (A) V to + V (B) -7.5 V to 7.5 V (C) -5 V to +5 V (D) V and 5 V OL.5 MCQ.54 Let the voltage at non inverting terminal be V, then after applying KCL at non inverting terminal ide we have 5 V + V V V ( 5) or V V If V wing from -5 to +5 V then V wing between -5 V to +5 V. Hence (C) i correct option. The logic function implemented by the following circuit at the terminal OUT i (A) P NOR Q (C) P OR Q (B) P NAND Q (D) P AND Q OL.54 From the figure hown below it may be eaily een upper MOFET are horted and connected to V dd thu OUT i only when the node i, ince the lower MOFET are horted to ground, node i only when input P

28 Page 8 GATE EC 8 and Q are. Thi i the function of AND gate. Hence (D) i correct anwer. MCQ.55 OL.55 Conider the following aertion. : For Zener effect to occur, a very abrupt junction i required. : For quantum tunneling to occur, a very narrow energy barrier i required. hich of the following i correct? (A) Only i true (B) and are both true but i not a reaon for (C) and and are both true but i not a reaon for (D) Both and are fale Hence option (A) i correct. MCQ.56 The two number repreented in igned complement form are P + and Q. If Q i ubtracted from P, the value obtained in igned complement i (A) (B) (C) (D) OL.56 MCQ.57 MB of both number are, thu both are negative number. Now we get ( 9) and ( 6) P Q ( 9) ( 6) 7 Thu 7 igned two complement form i () 7 Hence (B) i correct anwer. hich of the following Boolean Epreion correctly repreent the relation between,, PQR and M OL.57 (A) M ( PORQ) XOR R (B) M ( P ANDQ) X OR R (C) M ( P NORQ) X OR R (D) M ( P XORQ) XOR R The circuit i a hown below

29 Page 9 GATE EC 8 X PQ Y ( P+ Q) o Z PQ( P + Q) ( P+ Q)( P+ Q) PQ + PQ P 5 Q and M Z5 R ( P5Q) 5R Hence (D) i correct anwer MCQ.58 For the circuit hown in the following, I I are input to the 4: multipleer, R (MB) and are control bit. The output Z can be repreented by (A) PQ + PQ + QR (B) PQ PQR PQ + + (C) PQR + PQR + PAR + QR (D) PQR + PQR + PQR + QR OL.58 Hence (A) i correct anwer. Z IR + IR + IR + IR ( P + Q) R + PR + PQR + PR PR + QR + PR + PQR + PR The k Map i a hown below

30 Page GATE EC 8 Z PQ + PQ + QR MCQ.59 For each of the poitive edge-triggered J K flip flop ued in the following figure, the propagation delay i t. hich of the following wave form correctly repreent the output at Q? OL.59 ince the input to both JK flip-flop i, the output will change every time with clock pule. The input to clock i The output Q of firt FF occur after time T and it i a hown below The output Q of econd FF occur after time T when it get input (i.e. after T from t ) and it i a hown below

31 Page GATE EC 8 Hence (B) i correct anwer. MCQ.6 For the circuit hown in the figure, D ha a tranition from to after CLK change from to. Aume gate delay to be negligible hich of the following tatement i true (A) Q goe to at the CLK tranition and tay at (B) Q goe to at the CLK tranition and tay (C) Q goe to at the CLK tradition and goe to when D goe to (D) Q goe to at the CLK tranition and goe to when D goe to OL.6 The circuit i a hown below The truth table i hown below. hen CLK make tranition Q goe to and when D goe to, Q goe to Hence (A) i correct anwer. MCQ.6 A rectangular waveguide of internal dimenion (a 4 cm and b cm) i to be operated in TE mode. The minimum operating frequency i (A) 6.5 GHz (B) 6. GHz (C) 5. GHz (D).75 GHz OL.6 Cut-off Frequency i f c m n c ` + a j `b j

32 Page GATE EC 8 For TE mode, f c # 65. ` + 4 j `j GHz Hence (A) i correct option. MCQ.6 OL.6 MCQ.6 OL.6 MCQ.64 One end of a lo-le tranmiion line having the characteritic impedance of 75Ω and length of cm i hort-circuited. At GHz, the input impedance at the other end of tranmiion line i (A) (B) Reitive (C) Capacitive (D) Inductive Hence (D) i correct option. Z in Z ZL+ izotan( βl) o Z + iz tan( β l ) o L For ZL, Z in izo tan( βl) The wavelength i 8 λ c #. m or cm f 9 # β l π l π # π λ 5 Thu Z in izo tan π 5 Thu Z in i inductive becaue Z tan π o i poitive 5 A uniform plane wave in the free pace i normally incident on an infinitely thick dielectric lab (dielectric contant ε 9). The magnitude of the reflection coefficient i (A) (B). (C).5 (D).8 Hence (C) i correct option. μ e have η ε Reflection coefficient η η Γ η + η ubtituting value for η and η we have μo μo εε o r εo τ r ε 9 μo μo εε + o r ε ε 9 o + r + 5. ince ε r 9 In the deign of a ingle mode tep inde optical fibre cloe to upper cut-off, the ingle-mode operation i not preerved if (A) radiu a well a operating wavelength are halved

33 Page GATE EC 8 (B) radiu a well a operating wavelength are doubled (C) radiu i halved and operating wavelength i doubled (D) radiu i doubled and operating wavelength i halved OL.64 MCQ.65 OL.65 MCQ.66 OL.66 MCQ.67 In ingle mode optical fibre, the frequency of limiting mode increae a radiu decreae Hence r \ f o. if radiu i doubled, the frequency of propagating mode get halved, while in option (D) it i increaed by two time. Hence (C) i correct option. At GHz, the gain of a parabolic dih antenna of meter and 7% efficiency i (A) 5 db (B) 5 db (C) 5 db (D) 45 db Hence (D) i correct option. 8 λ c # f 9 # Gain G D p ηπ ` λ j 7. # π c m db Noie with double-ided power pectral denity on K over all frequencie i paed through a RC low pa filter with db cut-off frequency of f c. The noie power at the filter output i (A) K (B) Kf c (C) kπ f c (D) Hence (C) i correct option. PD of noie i N K...() The -db cut off frequency i f c...() πrc Output noie power i N 4RC N c m Kπf RC c Conider a Binary ymmetric Channel (BC) with probability of error being p. To tranmit a bit, ay, we tranmit a equence of three. The receiver will interpret the received equence to repreent if at leat two bit are. The probability that the tranmitted bit will be received in error i (A) p + p ( p) (B) p

34 Page 4 GATE EC 8 (C) ( p ) (D) p + p ( p) OL.67 At receiving end if we get two zero or three zero then it error. Let p be the probability of bit error, the probability that tranmitted bit error i Three zero + two zero and ingle one Cp + Cp ( p) p + p ( p) Hence (D) i correct option. MCQ.68 Four meage band limited to,, and repectively are to be multipleed uing Time Diviion Multipleing (TDM). The minimum bandwidth required for tranmiion of thi TDM ignal i (A) (B) (C) 6 (D) 7 OL.68 MCQ.69 OL.69 Bandwidth of TDM i (um of Nyquit Rate) [ ] 7 Hence (D) i correct option. Conider the frequency modulated ignal 5 co[ π# t+ 5 in( π# 5t) in( π# t)] with carrier frequency of 5 Hz. The modulation inde i (A).5 (B) (C) 7.5 (D) 5 Hence (B) i correct option. 5 e have θ i π t+ 5 in( π5t) in( πt) d i 5 ωi θ π + π5 co(π5 t) + 5π co(π t) dt Maimum frequency deviation i ω ma π( 5 # # ) f ma 5 fma Modulation inde i 5 f 5 m MCQ.7 The ignal co ωct+ 5. co ωmtin ωct i (A) FM only (C) both AM and FM (B) AM only (D) neither AM nor FM OL.7 Hence (C) i correct option.

35 Page 5 GATE EC 8 Common Data for Quetion 7, 7 and 7 : A peed ignal, band limited to 4 khz and peak voltage varying between +5 V and 5 V, i ampled at the Nyquit rate. Each ample i quantized and repreented by 8 bit. MCQ.7 OL.7 MCQ.7 OL.7 MCQ.7 OL.7 If the bit and are tranmitted uing bipolar pule, the minimum bandwidth required for ditortion free tranmiion i (A) 64 khz (B) khz (C) 8 khz (D) 4 khz Hence (B) i correct option. f m 4 KHz f fm 8 khz Bit Rate R b nf 8# 8 64 kbp The minimum tranmiion bandwidth i B Rb khz Auming the ignal to be uniformly ditributed between it peak to peak value, the ignal to noie ratio at the quantizer output i (A) 6 db (B) db (C) 48 db (D) 4 khz Hence (C) i correct option. cn m n db # db e have n 8 The number of quantization level required to reduce the quantization noie by a factor of 4 wo (A) 4 (B) 5 (C) 56 (D) 64 Hence (B) i correct option. A Noie \ L To reduce quantization noie by factor 4, quantization level mut be two time i.e. L. n 8 Now L 56 Thu L 5 Common data for quetion 74 & 75 : The following erie RLC circuit with zero condition i ecited by a unit impule

36 Page 6 GATE EC 8 function δ () t. MCQ.74 For t >, the output voltage vc ^th i OL.74 t t (A) ^e e h (B) te t (C) e t co t c m (D) e t in c riting in tranform domain we have V () c V () ^ + + h ( + + ) ince V() t δ() t " V() and Vc () ( + + ) or Vc () ( + ) + 4 G Taking invere laplace tranform we have V t e in t t c m Hence (D) i correct option. MCQ.75 For t >, the voltage acro the reitor i (A) t t _ e e i (B) e t co t in t c m c mg t m OL.75 (C) e t inc t m (D) e t co t c m Let voltage acro reitor be v R VR () V () ( + + ) ( + + ) ince v δ() t " V() we get VR () ( + + ) ( + ) + 4

37 Page 7 GATE EC 8 ( + ) ( + ) + 4 ( + ) + 4 or vr () t e co t e in # t t e co t in t G Hence (B) i correct option. Linked Anwer Quetion : Q. 76 to Q.85 carry two mark each. tatement for linked Anwer Quetion 76 & 77: A two-port network hown below i ecited by eternal DC ource. The voltage and the current are meaured with voltmeter V, V and ammeter. A, A (all aumed to be ideal), a indicated Under following condition, the reading obtained are: () -open, - cloed A, V 4.5 V, V.5V, A A () -open, - cloed A 4A, V 6 V, V 6V, A MCQ.76 OL.76 The z -parameter matri for thi network i (A) G (B) G (C) G (D) G From the problem tatement we have z v 6 5. Ω i i 4 z v Ω i i z v 6 5. Ω i i 4 z v Ω i i Thu z -parameter matri i

38 Page 8 GATE EC 8 z z z z G G Hence (C) i correct option. MCQ.77 OL.77 The h-parameter matri for thi network i (A) 67. G (B) 67. G (C) 67. G (D) 67. G From the problem tatement we have h v. 45 v i 5. h i 67. v i 5. From z matri, we have v zi + zi v zi + zi If v Then i z 5. h i z 5. or i i Putting in equation for v, we get v ( z z) i v h z z i v Hence h parameter will be h h h h G 67. G Hence (A) i correct option. tatement for Linked Anwer Quetion 78 and 79 : In the following network, the witch i cloed at t and the ampling tart from t. The ampling frequency i Hz.

39 Page 9 GATE EC 8 MCQ.78 The ample n ( ), n (,,,...) are given by (A) 5( e 5. n ) (B) 5e. 5n (C) 5( e 5n ) (D) 5e 5n OL.78 MCQ.79 OL.79 Current through reitor (i.e. capacitor) i + I I( ) e trc / Here, I( + ) V 5 5μA R k RC k # μ ec I 5e t μa VR # R 5e t V Here the voltage acro the reitor i input to ampler at frequency of Hz. Thu n n ( ) 5e 5e 5. n # For t > Hence (B) i correct anwer. The epreion and the region of convergence of the z tranform of the ampled ignal are (A) 5z, z < e 5 (B) 5z 5 5., z < e. 5 z e z e (C) 5z 5., z > e 5. (D) 5z z e z e 5, z e Hence (C) i correct anwer. ince n ( ) 5 e 5. n u( n) i a caual ignal It z tranform i Xz () 5 : 5. e z D 5z. z 5 e It ROC i e z > " z > e > 5 tatement for Linked Anwer Quetion 8 and 8: In the following tranitor circuit, VBE 7. V, r 5 mv/i E, and β and all the capacitance are very large MCQ.8 The value of DC current I E i

40 Page 4 GATE EC 8 (A) ma (C) 5 ma (B) ma (D) ma OL.8 For the given DC value the Thevenin equivalent circuit i a follow The thevenin reitance and voltage are V TH # 9 V + and total R TH k# k 667. kω k+ k MCQ.8 OL.8 ince β i very large, therefore I B i mall and can be ignored Thu I VTH VBE. E 7 ma RE k. Hence (A) i correct option. The mid-band voltage gain of the amplifier i approimately (A) -8 (B) - (C) -9 (D) -6 The mall ignal model i hown in fig below or g m IC m A/V IC. I V 5m 5 T V o gm Vπ # ( k k) Vin(. 5k) Vπ V 5 in A m 6V in Vo 6 V in E

41 Page 4 GATE EC 8 Hence (D) i correct option. tatement For Linked Anwer Quetion 8 & 8 : In the following circuit, the comparator output i logic if V> V and i logic n - n " " otherwie. The D/A converion i done a per the relation VDAC b Volt, where b n (MB), b, b and b (LB) are the counter output. The counter tart from the clear tate. / MCQ.8 OL.8 The table reading of the LED diplay i (A) 6 (B) 7 (C) (D) Hence (D) i correct anwer. e have V DAC n - - / bn b + b + b + b n or V DAC 5. b+ b+ b+ 4b The counter output will increae by from till V counter and V DAC i a hown below th > VDAC. The output of Clock bbbb V DAC

42 Page 4 GATE EC and when VADC 65. V (at ), the output of AND i zero and the counter top. The table output of LED diplay i. MCQ.8 OL.8 The magnitude of the error between V DAC and V in at teady tate in volt i (A). (B). (C).5 (D). Hence (B) i correct anwer. The VADC Vin at teady tate i V tatement for Linked Anwer Quetion 84 & 85 : The impule repone ht () of linear time - invariant continuou time ytem i given by ht () ep( ) tut (), where ut () denote the unit tep function. MCQ.84 The frequency repone H( ω ) of thi ytem in term of angular frequency ω, i given by H( ω) (A) (B) in ω + jω ω OL.84 (C) + jω Hence (C) i correct anwer. ht () e t u() t jωt Hjω ( ) hte () # dt (D) t j ω t ( + j ω) # # t e e dt e dt jω + jω ( + jω) MCQ.85 The output of thi ytem, to the inuoidal input t ( ) co tfor all time t, i 5. (A) (B) co(t.5 π) 5. (C) co(t.5 π) 5. (D) co(t.5 π)

43 Page 4 GATE EC 8 OL.85 Hence (D) i correct anwer. Hjω ( ) ( + jω) The phae repone at ω rad/ec i + Hj ( ω ) tan ω tan π.5π 4 Magnitude repone at ω rad/ec i Hjω ( ) + w Input i t () co( t) Output i # co( t. 5π) co[ t. 5π] Anwer heet. (C) 9. (B) 7. (A) 55. (A) 7. (B). (B). (A) 8. (D) 56. (B) 74. (D). (A). (A) 9. (C) 57. (D) 75. (B) 4. (A). (D) 4. (C) 58. (A) 76. (C) 5. (A). (C) 4. (C) 59. (B) 77. (A) 6. (B) 4. (A) 4. (C) 6. (A) 78. (B) 7. (C) 5. (C) 4. (B) 6. (A) 79. (C) 8. (B) 6. (A) 44. (B) 6. (D) 8. (A) 9. (C) 7. (D) 45. (C) 6. (C) 8. (D). (D) 8. (B) 46. (B) 64. (C) 8. (D). (C) 9. (*) 47. (B) 65. (D) 8. (B). (C). (A) 48. (C) 66. (C) 84. (C). (D). (C) 49. (C) 67. (D) 85. (D) 4. (A). (A) 5. (*) 68. (D) 5. (C). (D) 5. (C) 69. (B) 6. (D) 4. (B) 5. (C) 7 (C) 7. (C) 5. (B) 5. (C) 7 (B) 8. (D) 6. (A) 54. (D) 7 (C)

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