GATE EC : EL ECTRONI CS AND COM M UNI CATI ON ENGI NEERI NG. Du r at ion : Th r ee H ou r s M axi mu m M ar k s : 100

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1 GATE - EC : EL ECTRONI CS AND COM M UNI CATI ON ENGI NEERI NG Du r ion : Th r H ou r M i mu m M r k : Rd h fol l ow i n g i n r u c i on cr fu l l y.. All quion in hi ppr r of ojciv yp.. Thr r ol of 65 quion crrying mrk.. Quion hrough 5 r -mrk quion, quion 6 hrough 55 r -mrk quion.. Quion 8 nd 5 ( pir) common d quion nd quion pir (Q. 5 nd Q.5) nd (Q. 5 nd Q.55) r linkd nwr quion. Th nwr o h cond quion of h ov pir dpnd on h nwr o h fir quion of h pir. I f h fir quion in h linkd pir i wrongly nwr d or i unmpd, hn h nwr o h cond quion in h pir will no vlud. 5. Quion long o gnrl piud (GA). Quion 56-6 will crry -mrk ch, nd quion 6-65 will crry -mrk ch. Th GA quion will gin on frh pg. 6. Un-mpd quion will crry zro mrk. 7. Wrong nwr will crry NEGATI VE mrk. For Q. o Q.5 nd Q.56 - Q.6, / mrk will dducd for ch wrong nwr. For Q. 6 o Q. 5, nd Q.6 - Q.65, / mrk will dducd for ch wrong nwr. Th quion pir (Q. 5, Q. 5) nd (Q. 5, Q. 55) r quion wih linkd nwr. Thr will ngiv mrk only for wrong nwr o h fir quion of h linkd nwr quion pir i.. for Q. 5 nd Q.5, / mrk will dducd for ch wrong nwr. Thr i no ngiv mrking for Q. 5 nd Q.55..

2 SOLVED PAPER- (ELECTRONICS AND COMMUNICATION ENGINEERING - EC) Q. o Q.5 cr r y on m r k ch.. A ul in irc h wo wich, on wich ing h ground floor nd h ohr on h fir floor. Th ul cn urnd ON nd lo cn urnd OFF y ny on of h wich irrpciv of h of h ohr wich. Th logic of wiching of h ul rml () n AND g () n OR g n XOR g (d) NAND g r. Conidr vcor fild A ( ). Th clod loop li n ingrl A dl cn prd () ( A) d ovr h clod urfc oundd y h loop () ( A)dv ovr h clod volum oundd y h loop ( A)dv ovr h opn volum oundd y h loop (d) ( A) d ovr h opn urfc oundd y h loop. Two ym wih impul rpon h () nd h () r conncd in ccd. Thn h ovrll impul rpon of h ccdd ym i givn y () produc of h () nd h () () um of h () nd h () convoluion of h () nd h () (d) urcion of h () from h (). I n forwrd id pn juncion diod, h qunc of vn h dcri h mchnim of currn flow i () i n j c i on, nd uqu n di ff ui on n d rcominion of minoriy crrir () injcion, nd uqun drif nd gnrion of minoriy crrir rcion, nd uqun diffuion nd gnrion of minoriy crrir (d) rcion, nd uqun drif nd rcominion of minoriy crrir 5. I n I C chnology, dry oidion (uing dry oygn) comprd o w oidion (uing m or wr vpor) produc () uprior quliy oid wih highr growh r () infrior quliy oid wih highr growh r infrior quliy oid wih lowr growh r (d) uprior quliy oid wih lowr growh r 6. Th mimum vlu of unil which h pproimion in hold o wihin % rror i () 5 () 8 (d) 9 7. Th divrgnc of h vcor fild A ˆ yˆ z ˆ i () () (d) y z 8. Th impul rpon of ym i h() u(). For n inpu u( ), h oupu i () u( ) ( ) u( ) () (d) ( ) u( ) u ( ) 9. Th Bod plo of rnfr funcion G() i hown in h figur low. Gin (db) 8 (rd/) Th gin ( log G() ) i db nd 8 db rd/ nd rd/ rpcivly. Th ph i ngiv for ll. Thn G () i () () (d). In h circui hown low wh i h oupu volg (V ou ) if ilicon rnior Q nd n idl op-mp r ud? 5V _ () 5 V.7 V k _ 5 V 5 V ().7 V (d) 5 V Q Vou. Coni dr dl connc i on of r i or nd i qui vl n r connc i on hown l ow. I f l l lmn of h dl conncion r cld y fcor K, K > O, h l mn of h cor r pondi ng r quivln will cld y fcor of R R C R B R R c R A () k () k l/k (d) k

3 SOLVED PAPER- (ELECTRONICS AND COMMUNICATION ENGINEERING - EC). For 885 mi cr opr ocor, h fol l owi ng pr ogrm i cud. MVI A, 5H; MVI B, 5H; PTR: ADD B; DCR B; JNZ PTR; ADI H; HLT; A h nd of progrm, ccumulor conin () 7H H () H (d) 5H. Th i r of di gi l communi ci on y m i R ki/. Th modulion ud i -QAM. Th minimum ndwidh rquird for I SI fr rnmiion i () R/ Hz R/ 5 Hz () R/ khz (d) R/ 5 khz. For priodic ignl v() in co 6 in (5 /), h fundmnl frquncy in rd/ i () () 5 (d) 5 5. I n volg-volg fdck hown low, which on of h following mn i TRUE if h gin k i incrd? _ Vin V _ A _ Vou 8. Which on of h following mn i NOT TRUE for coninuou im cul nd l LTI ym? () All h pol of h ym mu li on h lf id of h j i. () Zro of h ym cn li nywhr in h -pln. All h pol mu li wihin. (d) All h roo of h chrcriic quion mu locd on h lf id of h j i. 9. Th minimum ign vlu of h following mri i () () (d). A polynomil f() wih ll cofficin poiiv h () no rl roo () no ngiv rl roo odd numr of rl roo (d) l on poiiv nd on ngiv rl roo. Auming zro iniil condiion, h rpon y() of h ym givn low o uni p inpu u() i U() Y() V f V ou _ k _ () T h i npu i mpdn c i ncr nd ou pu impdnc dcr. () T h i npu i mpdn c i ncr nd ou pu impdnc lo incr. T h i npu i mpdn c dcr nd ou pu impdnc lo dcr. (d) T h i npu i mpdn c dcr nd ou pu impdnc incr. 6. A nd-limid ignl wih mimum frquncy of 5kH z i o mpld. Accor di ng o h mpl ing horm, h mpling frquncy which i no vlid i () 5 khz () khz 5 khz (d) khz 7. I n M OSFET opring in h urion rgion, h chnnl lngh modulion ffc cu () n incr in h g-ourc cpcinc () dcr in h rnconducnc dcr in h uniy-gin cuoff frquncy (d) dcr in h oupu rinc () u() u( ). Th rnfr funcion i ().5 F () u() (d) u() V ( ) of h circui hown low V ( ) k V() V () F () 6 (d). A ourc v () V co h n inrnl impdnc of ( j). I f purly riiv lod conncd o hi ourc h o rc h mimum powr ou of h ourc, i vlu in hould () () 5 (d) 7

4 SOLVED PAPER- (ELECTRONICS AND COMMUNICATION ENGINEERING - EC). Th rurn lo of dvic i found o db. Th volg nding wv rio (VSWR) nd mgniud of rflcion cofficin r rpcivly (). nd. ().8 nd.. nd. (d). nd. 5. L g(), nd h() i filr mchd o g(). I f g( ) i ppl i d i npu o h(), hn h Four i r rnform of h oupu i () f f (d) () f / f 6. L U nd V wo indpndn zro mn Guin rndom vril of vrinc nd 9 rpcivly. Th proiliy P(V U) i () 9 () (d) L A n m n mri nd B n n m mri. I i givn h drminn (I m AB) drminn (I n BA), whr I k i h k k idniy mri. Uing h ov propry, h drminn of h mri givn low i () () 5 8 (d) 6 8. I n h circui hown low, if h ourc volg V 5: V hn h Thvnin' quivln volg in Vol n y h lod rinc R L i V S I () 9 89 j j6 5 V L _ ji V L () 8 (d) 6 9. Th opn-loop rnfr funcion of dc moor i givn w( ) V ( ). Whn conncd in fdck hown low, h pproim vlu of K h will rduc h im conn of h clod loop ym y on hundrd im comprd o h of h opn-loop ym i I R L. I n h circui hown low, h kn currn of h idl Znr diod i ma. To minin 5 V cro R L, h minimum vlu of R L in nd h minimum powr ring of h Znr diod in mw, rpcivly, r V V 5 V Z I Lod () 5 nd 5 () 5 nd 5 5 nd 5 (d) 5 nd 5. Th fol l owi ng r r ngmn coni of n i dl rnformr nd n nuor which nu y fcor of.8. An c volg V w V i pplid cro WX o g n opn circui volg V yz cro YZ. N, n c volg V yz V i pplid cro YZ o g n opn circui volg V w cro WX. Thn, V yz / V w, V w / V yz r rpcivly, W :.5 () 5/ nd 8/ Y () / nd 8/ / nd / (d) 8/ nd 8/. Two mgni clly uncoupld induc iv coil hv Q fcor q nd q h chon opri ng frquncy. Thi r r pc i v r i nc r R nd R. Whn conncd in ri, hir ffciv Q fcor h m opring frquncy i () q q () (/q )(/q ) (q R q R ) / (R R ) (d) (q R q R ) / (R R ). Th impul rpon of coninuou im ym i givn y h() ( ) ( ). Th vlu of h p rpon i () () (d). Th mll-ignl rinc (i.., dv B /di D ) in k offrd y h n-chnnl MOSFET M hown in h figur low, i poin of V B V i (dvic d for M: dvic rnconducnc prmr k n C o (W/L) A/ V, hrhold volg V TN V, nd nglc ody ffc nd chnnl lngh modulion ffc) I D X V B R L Z R() _ K V () () M () () 5 (d) ().5 () 5 5 (d)

5 SOLVED PAPER- (ELECTRONICS AND COMMUNICATION ENGINEERING - EC) 5 5. Th c chmic of n NMOS common-ourc g i hown in h figur low, whr pr of h iing ci r cui h n omi d for i mpl i ci y. For h n -chnn l M OSF ET M, h r nconduc nc g m ma/v, nd ody ffc nd chnnl l ng h modulion ffc r o nglcd. Th lowr cuoff frquncy in H z of h circui i pproimly V i R D k M C F () 8 () 5 (d) V R L k 6. A y m i dcr id y h di ffrni l qu ion d y dy 5 6 y( ) (). d d L () rcngulr pul givn y () ohrwi Auming h y() nd dy d rnform of y() i () ( )( ) ( )( ) () (d), h Lplc ( )( ) ( )( ) 7. A ym dcrid y linr, conn cofficin, ordinry, fir ordr diffrnil quion h n c oluion givn y y() for >, whn h forcing funcion i () nd h iniil condiion i y(). I f on wih o modify h ym o h h oluion com y() for >, w nd o () chng h iniil condiion o y() nd h forcing funcion o () () chng h iniil condiion o y() nd h forcing funcion o () chng h iniil condiion o j y () nd h forcing funcion o j ( ) (d) chng h iniil condiion o y() nd h forcing funcion o () 8. Coni dr wo i dn i cl l y di r i u d zr o-mn r ndom vr i l U nd V. L h cumul i v diriuion funcion of U nd V F() nd G() rpcivly. Thn, for ll vlu of () F() G() () F() G() (F() G()) (d) (F() G()) 9. Th DF T of vc or c d i h vc or. Conidr h produc c d d c p q r c d c d c d Th DFT of h vcor p q r i cld vrion of () () (d). Th ignl flow grph for ym i givn low. Th rnfr funcion Y( ) U( ) U() () 5 6 for hi ym i S - () (d) S Y(). I n h circui hown low h op-mp r idl. Thn V ou in Vol i V k k k V 5 V 5 V () () 6 k 8 (d) _ 5 V _ 5 V k V ou

6 6 SOLVED PAPER- (ELECTRONICS AND COMMUNICATION ENGINEERING - EC). I n h circui hown low, Q h ngligil collc or o-mi r ur i on vol g nd h diod dr op ngli gi l vol g cr o i undr for wr d i. I f V cc i 5 V, X nd Y r di gi l i gnl wi h V l ogic nd V cc logi c, hn h Booln pr i on for Z i Vcc. A vol g i n Vol i ppl i d cr o YZ. Auming idl diod, h volg murd cro WX in Vol, i () in () (in in )/ (in in )/ (d) for ll W k Y Z k _ X () XY XY X R R Q () XY (d) XY Z Diod Y. Thr cpcior C, C nd C who vlu r F, 5F, nd F rpcivly, hv rkdown volg of V, 5V, nd V rpcivly. For h inrconncion hown low, h mimum f volg in Vol h cn ppl i d cr o h comi n i on, nd h corrponding ol chrg in C ord in h ffciv cpcinc cro h rminl r rpcivly, ().8 nd 6 C C () 7 nd 9.8 nd (d) 7 nd 8 C 5. Thr r four chip ch of y conncd o 6 i ddr u hown in h figur low. RAM,, nd rpcivly r mppd o ddr RAM# B E RAM# B A-A9 E RAM# B 8 i d u E A A A RAM# B A A A5 Inpu S S E () CH-FFFH, CH- FFFH, CH-FFFH, CH-FFFH () 8H-FFFH, 8H-FFFH, 8H-FFFH,8H-FFFH 5H -8FFH, 5H-8FFH, 5H-8FFH, 55H-58FFH (d) 8H-BFFH, 8H -BFFH, 8H-BFFH, 8H-BFFH

7 SOLVED PAPER- (ELECTRONICS AND COMMUNICATION ENGINEERING - EC) 7 6. I n h circui hown low, h ilicon npn rnior Q h vry high vlu of. Th rquird vlu of R in k o produc I C ma i R 6k R () () (d) 5 Q V CC V I C R E 5 7. L U nd V wo i ndpndn nd i dnicl l y di r i u d r ndom vri l uch h P(U ) P(U ). Th nropy H (U V) in i i () () (d) log COM M ON DATA QUESTI ONS Com m on D for Qu i on 8 nd 9: Bi nd r rnmid wih qul proiliy. A h rcivr, h pdf of h rpciv rcivd ignl for oh i r hown low. pdf of rcivd ignl for i.5 pdf of rcivd ignl for i - 8. I f h dcion hrhold i, h BER will () 8 () (d) 6 9. Th opimum hrhold o chiv minimum i rror r (BER) i () () 5 (d) Com m on D for Qu i on 5 nd 5: Conidr h following figur V S _ 5 A V I S 5. Th currn I in Amp in h volg ourc, nd volg V in Vol cro h currn ourc rpcivly, r (), () 8, 8, (d), 5. Th currn in h rior in Amp i () (). (d) L I NK ED ANSWER QUESTI ONS S m n for L i nk d Anw r Qu i on 5 nd 5 : A monochromic pln wv of wvlngh 6m i propging in h dircion hown in h figur low. E,E r nd E dno incidn, rflcd, nd rnmid i lcric fild vcor ocid wih h wv. E i H i K i i r H r K r z 9. E r H k r. r.5 5. Th ngl of incidnc, nd h prion for E r i ( z) E j () 6 nd ( ˆ ˆ ) z V / m z E j () 5 nd ( ˆ ˆ ) z V / m ( z) E j 5 nd ( ˆ ˆ z ) V / m z E j (d) 6 nd ( ˆ ˆ ) z V / m 5. Th prion for Er i ( z) E j (). ( ˆ ˆ ) z V / m z E j () ( ˆ ˆ ) z V / m ( z) E j. ( ˆ ˆ ) z V / m ( z) E j (d) ( ˆ ˆ ) z V / m S m n for L i nk d Anw r Qu- i on 5 nd 55 : Th digrm of ym i hown low. A ym i dcrid y h -vril quion u E X AX B u; y CX Du S S y

8 8 SOLVED PAPER- (ELECTRONICS AND COMMUNICATION ENGINEERING - EC) 5. Th -vril quion of h ym hown in h figur ov r () X X u () y X u X X u (d) y Xu X X u y X u X X u y X u 55. Th rniion mri A of h ym hown in h figur ov i () () (d) GENERAL APTI TUDE (GA) QUESTI ONS Q.56 o Q.6 cr r y on m r k ch. 56. Choo h grmmiclly CORRECT nnc: () Two nd wo dd four. () Two nd wo com four. Two nd wo r four. (d) Two nd wo mk four. 57. S m n : You cn lwy giv m ring whnvr you nd. Which on of h following i h infrnc from h ov mn? () Bcu I hv nic cllr un. () Bcu I hv r lphon fciliy. Bcu frind in nd i frind indd. (d) Bcu you nd no py owrd h lphon ill whn you giv m ring. 58. I n h ummr of, i n Nw Dl hi, h mn mprur of Mondy o Wdndy w C nd of Tudy o Thurdy w C. I f h mprur on Thurdy w 5% highr hn h of M ondy, hn h mprur in C on Thurdy w () () 6 (d) 9 6. Thy wr rqud no o qur r l wih ohr. Whi ch on of h fol lowing opion i h clo in mning o h word qur r l? () mk ou dig ou () cll ou (d) fll ou Q.6 o Q.65 cr r y w o m r k ch. 6. A cr rvl 8 km in h fir qurr of n hour, 6 km in h cond qurr nd 6 km in h hird qurr. Th vrg pd of h cr in km pr hour ovr h nir journy i () () 6 (d) 6. Find h um o n rm of h ri n 99 n () () 8 n n n (d) n 8 6. S m n : Thr wr diffrn rm of frdom movmn i n col oni l I ndi cr r i d ou y h modr, lirl, rdicl, ocili, nd o on. Which on of h following i h infrnc from h ov mn? () Th mrgnc of nionlim in colonil I ndi ld o our I ndpndnc. () N ionli m i n I ndi mr gd in h con of coloni lim. Nionlim in I ndi i homognou. (d) Nionlim in I ndi i hrognou. 6. Th of vlu of p for which h roo of h quion p(p l) r of oppoi ign i () (, ) () (, ) (, ) (d) (, ) 65. Wh i h chnc h lp yr, lcd rndom, will conin 5 Surdy? () 7 () Compl h nnc : Dr mik. () commi () o commi commi d (d) commi i ng 7 (d) 5 7 AN SWERS.. (d).. () 5. (d) 6. () 7. (d) (). (). (). (). (). () 5. () 6. () 7. (d) ().. (). (d).. () 5. (d) () (). ().. (). () 5. () 6. () 7. (d) 8. (d) 9. (). ().. (). (d). 5. (d) () 5. (d) () 55. () 56. (d) () 6. () (d) 6. (d) 6. () 65. ()

9 SOLVED PAPER- (ELECTRONICS AND COMMUNICATION ENGINEERING - EC) 9 EXPL ANATI ONS. L u coni dr h wi ch A nd B nd ul Y. Swich cn poiion up () or down () Sring wih oh A nd B in up poiion. L h ul OFF. Now inc B cn opr indpndnly whn B go down, h ul go ON A B Y up () up () OFF up () down () ON Now kping A in down poiion whn B go down, h ul will go OFF. A B Y down () up () ON down () down () OFF find ruh l corrpond o XOR g.. Hnc, for vcor fild A( r) A A d. d ccording o Sok horm. h ( ) h ( ). Uing h concp of virul ground in n oprionl mplifir, w cn h volg h poin o zro vol inc h non invring rminl i groundd.. Onc V A, V C will lo zro. W know h for ilicon n p n rnior, V BE V B V E.7 V Sinc, V B V E.7 V Hnc h oupu volg i h m h mir volg o, V ou.7 V R R C R C R R A R B R B R c h ( ) h() h () h (). Du o pplicion of volg (forwrd i minoriy crrir r injcd from ihr id of diod on uqun diffuion k plc nd finlly rcominion. I njcion nd uqun diffuion nd rcominion of minoriy crrir 5. A during dry oidion, quliy of oid i uprior i do no con i n ul l r whi ch i r poni l for coninmion/impuriy u imulnouly lowr h growh r 6. in lim limin wihin % of rror A yy zz A 8. A h() (f) inpu A A y A y z rpon () () u() ( I) d d z ( ) u( ) ( ) 9. log k k.6 d d T() 8 ( ) wo pol origin R c R R R R R c R R R c R R R c R A R i cld y fc k k R R R R k k(r R R ) R R c c o lmn corrponding o r quivlnc will d y fc k.. Accumulor chng follow (5 5 )H A h nd of Loop ccumulor conin H ADI H A ( ) 7H. Bi r givn R K i/cond M odulion -QAM No. of i/ymol 5[log ] Symol r R 5 k ymol/cond Finlly w r rnmiing ymol. E T rnmiion ndwidh R(ymol r ) R B T ( ) 5( ) For B T o minimum, h o mimum R R B T 5 Mimum vlu of i which i roll off fcor LCM of numror. LCM of T, T, T will : HCF of dnominor. Ovrll im priod c. H rmonic frquncy rd/c.

10 SOLVED PAPER- (ELECTRONICS AND COMMUNICATION ENGINEERING - EC) 5. I npu I ndpndnc of volg-volg fdck circui i ( A k) Z i i nii l i npu i mpdnc (wi hou fd ou pu I mpdnc of volg-volg fdck circui Z ( A k) Z iniil oupu impdnc (wihou fdck) H nc, A K i incrd, h inpu impdnc wi ll incr nd oupu impdnc will dcr. 6. Hr f m 5KHZ f > f m KHZ B,C,D opion r grr hn KHZ K VGS V ( V DS) n ou pu r i nc i givn y r...() ID VDS ID k ' n V GS V...() VDS r I D / dv DS kn V G V L For I dl c I D k ' n V G V L ID VDS r 7. I D 8. Coni dr op i on A: I n which ll h pol li on h lf of j i which ify cul l LT ym. Op i on B: For l cul ym, hr r no rricion for h poiion of zro on pln. Op i on C: ru. Op i on D: Roo of chrcriic quion r ll clod loop pol nd hy ll lin on h lf id of h j i. 9. A [6 9] 5 [5 ] [5 ]. A which, impli ihr of h ov ign vlu qul o zro. I my on or wo ngiv ign vlu. f ( n) I f compl roo r in vn no. (in pir) hn h rl roo will lo vn. opion i wrong. from h quion, A no. of roo Produc of roo Produc of no. < ihr or no <. B i Produc of roo: * * ZZ,ZZ Z Z which i no poil. H () h() u() u( ) inpu V( ) Y( ) oupu u () h () u () u () r (). Tking L plc rnformion of h circui, u V(S).6 S V(S) By pplying volg dvidr rul: V () V ( ) V ( ). Z i ( j ) Z L 5. Th rflcion co-fficin i log db log db;. Rlion wn nd VSWR i S g() 6. Gi vn: h() g( ) ( ) F [r()] F [h() g ()] H( ) G( ) f f f V ( ) A w know f U & V wo i ndpndn & i dn icl, di ri ud rndom vril U & V r I.I.D Noion o idnic proiliy dniy funcion U ~ N (, / ) Vrinc Mn Sign of guin diriuion rndom vril V N, / 9. To fi nd: P (V > U) Solu i on: V O U O P / / Rrrng h prolm

11 SOLVED PAPER- (ELECTRONICS AND COMMUNICATION ENGINEERING - EC) V EX E E V O L dno V O X V E E E V 9 9 U O Y 9 9. hn X & Y com X ~ N (, ). normlid diriuion (Guin) Y ~ N (, ) normlid Guin di riud. You cn cl r l y. H ow hy cm nor ml i d diriuion, w know h normlid diriuion h zro-mn & vrinc. U E y E E U U E y E E U. Quion rduc o: P (X > Y) P (X Y > O) A l, Z X Y, i i ju linr cominion rndom vril which i guion diriuion wih mn O & vrinc. hir Linr cominion i lo guin P (Z > O) No : By uing cnrl limi horm, no hr mn will E Z mn rmin m & vrinc com n im of ruling rndom vril, o figur will cm f z (z) z o mn 7. Gi vn: A : m n mri To find: d d(m) B : n m mri d (I m AB) d (I n BA) I K : K K idnify mri y Anl yi : W will rk mri m o mch (I m AB) Pl n:. A pr nlyi pr w will rk mri m ino um of I m nd AB. Thn u d (I m AB) d (I m BA) Cr r ying ou pl n:...() Now w will rk cond mri in RHS of ov follow Uing () ino (), w g I A nd B L m I A B n Bu w r givn h d (I m AB) d (I n BA)...()...() d(i A B ) d I d ( ) { I } d (5) 8. Givn: V 5.V j V L V S ~ I j I 5 { drminn of clr i h m clr} j6 5 V L I R L To find: Thvnin volg cro L od rionc Solu i on * For V h opn i. j V L V S ~ I j I j6 5 opn hi rminl V L I R L

12 SOLVED PAPER- (ELECTRONICS AND COMMUNICATION ENGINEERING - EC) * Opning, hn I * Whn I, hn ji {volg ourc will hor circui) Circui cm V L j6 5 j V S ~ V I L I V I j V VL j j V TH * V TH V L cu no-currn flowing hrough circui. V TH j V j V j j From rcngulr domin o polr domin. 9. Gi vn: 9º 5 º 5 5 VTH 8 9º Opn loop rnfr funcion of dc moor R(S) w( ) V ( ) K V (S) Topic : P conrollr wih uniy fd ck w( ) For m ul: For fir ordr ym loop rnfr funcion i C( ) K w( ) compring wih R( ) T V ( ) T opn loop Now for clod loop ovrll rnfr funcion i givn y K w( ) R( ) K K K K (K ) Dividing numror nd dnominor y K Now K w( ) K R( ) K So T clod loop (By compring from formul) K In Quion givn h im conn of clod loop ym i im of im conn of opn loop ym T T o clod loop opnloop K K K 99 K 9.9 K pproim vlu. I I z I L IS I I z I L Two rm condiion: I f I z (min),hn I L (m) If I z (m)hn I L (min) V I z (m) I 5 5 ma I z (min) I I L (m) I z I L V 5V I L (m) I I z (min) I I z (5 ) ma R L (min). c : V 5 K 5 I (m) L P z V z I z (m) 5 5 ma 5 mw So, Vyz V w V M V w.5 5V M Vyz Vyz 5.8 v. Vyz /Vw. nd c: Vyz V Vy 5v.8 M Now, Vw Vy z 5 v M.5 Vw /Vyz. L h ffciv Q fcor i q hn i cn wrin uing inducnc nd rinc of quivln circui. q Lq (L L ) Rq R R Now w uiu h vlu of L nd L in rm of q nd q qr qr q qr qr R R. A h() ( ) ( ) r() h() u() [( ) ( )] u() r() u ( ) u ( ). I D µ w co (V V ) T L V B V ID ID µ w co (V V T ) V V L D W µco V VT L ( ) dv V B 5K 6 I I D 6 6

13 SOLVED PAPER- (ELECTRONICS AND COMMUNICATION ENGINEERING - EC) 5. w L CR q w L 6 k k f L 6 f L ~ Sinc n() cn wri n in funci on of uing p funcion () () ( L) w nd o () lplc rnform () () d y( ) L d( ) Y() d y( ) dy L 6y d d y() y() 6y() () y() ( ) 5 6 ( )( ) 7. Gi vn: A linr conn cofficin, fir ordr diffrnil quion of y() forcing funcion () iniil condiion : y() y() > Fi nd ou : y(), y chnging h vlu of () nd y() Anlyi : L h diffrnil quion i dy py d () y() funcion of () nd y() f((), y()) L find h rlion wn y() nd () dfin ingring fcor I F. I.F. Pd I.F. I.F. I.F. i indpndn of n() nd y() Thn y() So for find y() I.F. y() ni.f. d y y() ni.f. d y I.F. So for g y(), chng h n() y (), nd y() wih y() 8. Gi vn: Two r ndom vr i l (R.V.) U nd V; I dn i cl l y dir iu d. M n: E (U) nd E(V) Cumuliv diriuion funcion (CDF): F U () F() F V () G () To fi nd: F() G() nd (F() G()) Anlyi : I dn i cl l y di r i ud R.V. U nd V mn hi r proiliy dniy funcion(pol) will om. And CDF i h ingrion of polf. So hir CDF will lo om Hnc Pl n: F U () F V (). Fir find F() G(); Thn chck i poiiviy or ngiviy.. Scondly find (F() G()); Thn chck i poiiviy or ngiviy. Cr r ying ou pl n: W know h F U () F() Pr (U )...() nd F V G() Pr(V )...() Now, conidr F V () F V () {From () nd ()} F() G() {From () nd ()} Pr(U ) Pr(V ) Now, P(V ) P V U hi rul ino ov prion {From () nd ()}...() F() G() Pr(U ) Pr V...() W know h Pr(U ) F U ()...(5) nd Pr V FV...(6) From nlyi cion w hv F U () F V ()...(7) From (6) nd (7) FV FU...(8) Uing (5) nd (6) ino () F() G() F u ( ) F...(9) v From (8) nd (9), w hv F() G() F U () FU Uing () ino ov F() G() F() F...() Propry of CDF: CDF i non-dcring funcion. C : i v ( ) F() F { Non-dcring funcion} F() F So from () C : i v ( ) F G...() F() F F() F So from () { Non-Ngiv funcion} F G...()

14 SOLVED PAPER- (ELECTRONICS AND COMMUNICATION ENGINEERING - EC) So from c nd c, rul our nwr dpnd on poiiviy nd ngiviy of. So for our nwr i opion (B); Bu for our nwr i opion (A). Bu no lwy (A) nd (B) o w rjc h wo opion. Now w hv o find om compc form for our nwr which will ru for ny vlu of. i.. for poiiv nd ngiv. C : From () F() G() Muliply y, w g C : From () F() G() Muliply y, w g (F( ) G( ))...() So from () nd () w hv F G...() F G for ll Opion (D) i corrc nwr. E m pl : A Gui on rndom vr il wi h mn ZERO h following proiliy dniy funcion (plf) F Th CDF will (pproimly) G( ) Conclui on: F k F( ) G( ) / f d F ( ) { non-dcring funcion} Th imporn poin o rmmr in quion i h CDF funcion i non-dcring funcion. 9. Gi vn: DFT [ c d] []...() c d d c p q r c d c d c d To find: DFT [p q r ]?...() Anl yi : W know h DFT [ (n) (n)] (K) (K)...() whr rprn circulr convoluion nd (k) DFT [ (n)]...() (k) DFT [ (n)]...(5) w know h cir culr convol u ion cn found y MATRI X METHOD M ATRI X M ETH OD: L wo qunc T T ( n) (),,(),... (N) colum vcor ( n) (), (),... (N) colum vcor Dign mri y y uing qunc (n) () (N) (N )... () () () (N).. () ()... ()..... M (6)... (N ) (N ) (N ) (N ) (N) (N) (N ) (N )... () Now circulr convoluion i givn y (n) * (n) M (n)...(7) Pl n:. Dign mri M y uing vcor [ c d]. Find circulr convoluion uing quion 7 Cr r ying our pl n: Uing vcor [ c d] dign mri M d c d c M c d d c Now circulr convoluion of [ c d] wih i lf. d c T T d c c d c d c d c d c d Tk rnpo on oh id d c d c c c c d c d d d d c from 8 nd, w g p q r c c d d Tk DFT oh id DFT [p q r ] DFT c c d d DFT [ c d] DFT [ c d] [] [] DFT...(8) p q r Elmn wi muliplicion...(9) Opion (A) i h corrc nwr Conclui on: Th imporn poin o nod i h qunc cn wri n vcor. So vcor nd qunc wr m hing.

15 SOLVED PAPER- (ELECTRONICS AND COMMUNICATION ENGINEERING - EC) 5. V(S) Forwrd ph Loop S S P S, S S P S L S L S S S L S L S S T(S) S S S S S S 6S S. K k V k V 5 5V k k S 5S 6S 5V 5V V ou V(S) V ou v v Gin of Gin Gin of non invry of non invry mp () invry mp () mp () [ ] v 8v. V CC X. D for ll W z. y cm X Y Z in X Y ~ K Y Z X W No : All diod conduc only don ngiv hlf. XW i ymmricl poin o volg cro XW i zro for ll im.. Gi vn vl u: Cpcinc Vlu Volg Brkdown C µf V C 5µF 5V C µf V. Gi vn ci r cui : To fi nd: A C C C M. f volg in vol h cn pplid cro h cominion nd Corrponding ol chrg i µc. Dvii ng pl n: () W wi ll fir clcul qui vl n cpci nc of givn figur. () By cl cul ing cpci nc, w cn chck whi ch nwr cn h oluion, i rduc your ffor in olving prolm. Thn pply h rmining nwr for rmining opi on. Solving: Equivln cpcinc, C & C r in ri nd w know h whn cpcinc r in ri quivln CC cpcinc C C & whn wo cpcior r in prlll hn hir ddiion C C C C C * C C C C C C 5µF µf µf..85µf 5µF µf Now chck h opion y uing formul CV ().8.85 C 6 C (opion () i wrong) hnc c opion cn righ Now whn 7V () 7V.85 µf 8µc 9µC { B i hnc d opion i righ. only c & d r lf. Now pply 7V fir in givn circui, whn volg cro AB i 7V hn C cn hndl i roz m rkdown volg cro i Y. nd cro A (V ) (V ) C C B B hy r in K Z 7V ri o chrg cro hm will m.

16 6 SOLVED PAPER- (ELECTRONICS AND COMMUNICATION ENGINEERING - EC) Q Q C V C V C V C V [V V 7V] C V C (7 V ) C V 7C C V 7C V C C 7 V V V V 5 nd V 7 V 7 V 5V A whn w k 7V hn for h V V & V 5V, u m volg cro V cn V [cu ov which i rkdown]. V V Bu, whn w k 7V hn V hv o 5V which i no poil hnc d i lo wrong. Only opion lf i c Bu, I will how h i i lo righ. Whn V AB. V Bu in cpcior A V C C C V AB C V C C So, don pply rinc volg mhod in o cpcior on, if you do h hn you will oin D nwr, u which i wrong. 5. A 5 A A A A A A 9 A 8 A 7 A 6 A 5 A A A A A RAM RAM RAM RAM RAM RAM RAM 8H BFF H 8H BFF H 8H FF H RAM 8H BFF H L pln o olv prolm 7. U X V r wo indpndn nd idniclly diriuion rndom vril AB B A C C B 6 volg cro C.8 V V V C C.8 C C [poil rkdown volg i V]. 8V [poil rkdown volg cro C i 5V)] C V.8 C C hnc opion D i corrc V [poil rkdown volg cro C i V] *Vr i fi c i on: A I lrdy howd h only i ru no on l. Con cl ui on : volg cro mhod cpcinc i no m volg cro mhod rinc. For drmin volg cro rinc w ju do w wn o drmin cro R & R o p u (u) ( u ) ( u ) i mi lrl y p v (v) ( ) ( ) Z (U V) P z (z) P u (u) P v (u) ( z ) ( z) ( z ) So nropy H(z) H (U V) 6 kr P log P log P P P log log log VCC V IC ma A R R B V B V R R V R R V AB AB R R 5 E

17 SOLVED PAPER- (ELECTRONICS AND COMMUNICATION ENGINEERING - EC) 7 8. A I C I E inc B I B VB V BE R E I E V BE R E I C V B.7 5. R R V B.V V R R 6 k R. (6 R ) R R. 6 k.8 Pd of rviw i Pd of rviw i.5 5. (C) Currn hrough A] 5. (D) [I A, V ] 5. Gi vn: Elcric fild vcor of monochromic pln wv. H i E i K i i r E r K r 9.º K H r r. E r.5 9. y y.5 y Solving (i) nd (ii) 5 y (i)...(ii) So opimum rio o chiv minimum i r (BER) 5 y y n 5 Topi c: Z 6 µm K H rd/m Pln wv propgion (Elcro mgnic) For mul: Snll lw, Er in i Er in Solu i on: To find h ngl of incidnc u nll lw. E r in i Er in. in i.5 in9. i. 5, i h dird incidnc ngl. To find h incidnc Elcric fild vcor, w nd o find h propgion conn fir. W cn rolv K i ino wo componn hown in h figur. K K O in i Bi rror r V S 5 A V V Applying KCK mod (V ) I S I S 5 Currn hrough A i K z K O co i K KO in i ; K KO co Qi w KO KO Now h ph rm cn givn y j zz j coi in iz j z...() Th componn coniuing h mpliud pr of Ei r z E i K i V 5 V V V i

18 8 SOLVED PAPER- (ELECTRONICS AND COMMUNICATION ENGINEERING - EC) Ei o Eˆ Ezzˆ E co i ˆ E in i zˆ E ˆ ˆ z v/m...() Thrfor, h prion for E i cn oind from () nd () quion 5. Gi vn: E j z ˆ ˆ z v/m Ei Elcric fild vcor of monochromic pln wv. K i E i i r E r 9.i K r K E E. r E.5 r Th ph rm will j z z j cor in r z j z...() Th mpliud rm cn oind y rolving E r ino wo componn z Ezo E r Eo E r E ˆ Ez z rflcion cofficin ˆ r ˆ E z E in co T ˆ r r.e ˆ ˆ z v/m...() Thu h prion for E r cn oind form () nd (), E j z. ˆ ˆ z V/m E r Topi c: Z 6 µm K rd/m Pln wv propgion (Elcromgnic) For mul: For n oliqu incidnc h rflcion cofficin i µ µ co co i co co i T co co µ µ co co Hr Solu i on: i µ µ µ 7 H/m ;.5 Fir w find h ngl of incidnc i from nll lw follow r in i r in On uiuing h vlu w g i 5 Th rflcion cofficin i, T co9. co5º.5. co9. co5º.5 To find h rflcd fild vcor E r,w nd o find h propgion conn, for rflcd wv in mdium. z K co r r k in r K r 9º i r i 55. Gi vn: Uing d of prviou quion S rniion mri: A Fi nd ou : A, which i givn L [[SI A] ] Solu i on SI A S S S [SI A] king Lplc I nvr S S S S S S S S S L [SI A] L L S L L S S