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1 SETION A (75 marks). This quesin cnsiss f TWENTYFIVE subquesins (..5) f ONE mark each. Fr each f hese subquesins, fur pssible alernaives (A,B, and D) are given, u f which ONLY ONE is crrec. Indicae he crrec answers in he bxes crrespnding he quesins nly n he FIST shee f he answer bk.. In he circui f Fig.P., he vlage v() is a b e e (b) a b ae be (d) a b e e a ae be b Ω e a V() H Ω e b. In he circui f Fig.P., he value f he vlage surce E is 6 V (b) 4 V 6V (d) 6 V V V 0V V E=? V 4V 5V 0V s s L = f =, L f =, h ( ) = f ( τ ) g ( τ ) dτ. s.3 Given ha ( ) ( ) ( ) L h is s s 3 ( s ) ( s ) s s s 3 ( s 3) ( s ) (b) s 3 (d) Nne f he abve 0 V.4 In he differenial amplifier f Fig.P.4, if he surce resisance f he curren surcei EE is infinie, hen he cmmnmde gain is zer (b) infinie V in Vin indeerminae (d) V V in in V T I EE V EE

2 .5 In he circui f Fig.P.5, V is V (b) V V (d) 5 V V V 5V.6 Inrducing a resisr in he emier f a cmmn amplifier sabilizes he dc peraing pin agains variains in nly he emperaure bh emperaure and β (b) nly he β f he ransisr (d) nne f he abve.7 The curren gain f a biplar ransisr drps a high frequencies because f ransisr capaciances (b) high curren effecs in he base parasiic inducive elemens (d) he Early effec.8 An amplifier wih resisive negaive feedback has w lef halfplane ples in is penlp ransfer funcin. The amplifier will always be unsable a high frequencies (b) will be sable fr all frequencies may be unsable, depending n he feedback facr (d) will scillae a lw frequencies.9 If he pamp in Fig.P..9, is ideal, hen v, is zer sinω (b) ( V V ) sinω ( V V ) sinω (d) ( V V ) V sinω V sinω V.0 The cnfigurain f Fig.P..0 is a precisin inegrar (b) Harley scillar Buerwrh highpass filer (d) Wienbridge scillar V

3 . Assume ha he pamp f Fig.P. is ideal. If vi is a riangular wave, hen v will be square wave (b) riangular wave parablic wave (d) sine wave V V. The Furier Transfrm f he signal ( ) and B are cnsans: Bf Ae (b) Bf Ae.3 A sysem wih an inpu x ( ) and upu ( ) y ( ) = x ( ). This sysem is linear and imeinvarian nnlinear and imeinvarian x = e 3 is f he fllwing frm, where A A Bf (d) Ae Bf y is described by he relain: (b) linear and ime varying (d) nnlinear and imevarying.4 The ampliude mdulaed wave frm s ( ) = A Km ( ) ideal envelpe deecr. The maximum magniude f 0 ( ) Which f he fllwing culd be he deecr upu? csω is fed an c a Am c ( ) (b) A Km ( ) A Km ( ) c a c (d) A Km ( ) c Km is greaer han. a a.5 An 8 bi successive apprximain analg digial cnverer has full scale reading f.55 V and is cnversin ime fr an analg inpu f V is 0µs. The cnversin fr a V inpu will be 0 µs (b) 0 µs 40 µs (d) 50 µs.6 The number f hardware inerrups (which require an exernal signal inerrup) presen in an 8085 micrprcessr are (b) 4 5 (d) 3.7 The ms cmmnly used amplifier in sample and hld circuis is a uniy gain invering amplifier (b) a uniy gain nninvering amplifier an invering amplifier wih a gain f 0 (d) an invering amplifier wih a gain f 00

4 .8 The number f cmparars in a 4 bi flash AD is 4 (b) 5 5 (d) 6.9. Fr he lgic circui shwn in Fig.P.9, he required inpu cndiin (A,B,) make he upu (X)= is A, 0, B (b) 0, 0,,, (d) 0,, x.0. In he 8085 micrprcessr, he ST6 insrucin ransfers he prgram execuin he fllwing lcain 30 H (b) 4 H 48 H (d) 60 H.. The magniudes f he pencircui and shrcircui inpu impedances f a ransmissin line are 00Ω and 5Ω respecively. The characerisic impedance f he line is, 5Ω (b) 50Ω 75Ω (d) 00Ω.. A TEM wave is inciden nrmally upn a perfec cnducr. The E and H fields a he bundary will be, respecively. minimum and minimum minimum and maximum (b) maximum and maximum (d) maximum and minimum.3. The frequency range fr saellie cmmunicain is KHz 00 KHz (b) 00 KHz 0 KHz 0 MHz 30 MHz (d) GHz 30 GHz λ λ λ.4. If he diameer f a diple anenna is increased frm, hen is bandwidh increases gain increases (b) bandwidh decreases (d) gain decreases L.5 The circui f Fig.P.5 represens a S lw pass filer (b) high pass filer band pass filer ~ V S L L V (d) band rejec filer

5 . This quesin cnsiss f TWENTYFIVE subquesins (..5) f ONE mark each. Fr each f hese subquesins, fur pssible alernaives (A,B, and D) are given, u f which ONLY ONE is crrec. Indicae he crrec answers in he bxes crrespnding he quesins nly n he SEOND shee f he answer bk.. The eigen values f he marix are ,,, (b), 3,, 4, 3,, 4 (d) Nne f he abve.. Use he daa f Fig.. The curren i in he circui f Fig.(b) is A (b) A 4A (d) 4A 0V A I=? 4 0V.3. Fr he circui in Fig.P.3, he vlage v is Ω Ω V V (d) Nne f he abve (b) V 4V Ω v V.4. A linear ime invarian sysem has an impulse respnse cndiins are zer and he inpu is 3 e, he upu fr > 0 is e, > 0. If he iniial 3 e e (b) 5 e 3 e e (d) Nne f he abve.5. In he circui f Fig.P.5, assume ha he ransisr is in acive regin. I has a large β and is baseemier vlage is 0.7V. The value f I c is Indeerminae since c is n given (b) ma 5 ma (d) 0 ma 0kΩ 5kΩ 5V I 430Ω

6 .6. If he pamp in Fig.P.6, has an inpu ffse vlage f 5 mv and an penlp vlage gain f 0,000, hen v will be 5V 0V (b) 5 mv V 5 V r 5 V (d) 50 V r 50 V 5V.7. Fr he lgic circui shwn in Fig.P.7, he simplified Blean expressin fr he upu Y is AB A B (b) A B (d).8. Fr he 4 bi DA shwn in Fig.P.8, he upu vlage v is K 7K Y 5V V 5V V 0 V (b) 5 V 4 V (d) 8 V V.9. A sequenial circui using D flipflp and lgic gaes is shwn in Fig.P.9, where X and Y are he inpus and Z is he upu. The circui is X Y LK D Q Q Z Z S FlipFlp wih inpus X = and Y = S (b) S FlipFlp wih inpus X = S and Y = J K FlipFlp wih inpus X = J and Y = K (d) J K FlipFlp wih inpus X = K and Y = J

7 Jin discussin f his es paper a hp://frum.gaemenr.cm.0. The cnens f egiser (B) and Accumular (A) f 8085 micrprcessr are 49H and 3AH respecively. The cnens f A and he saus f carry flag (Y) and sign flag (S) afer execuing SUB B insrucins are A = F, Y =, S = (b) A = 0F, Y =, S = A = F0, Y = 0, S =0 (d) A = F, Y =, S =.. In Fig.P., he J and K inpus f all he fur FlipFlps are made high. The frequency f he signal a upu Y is F=0kHz J K Q J Q J Q J Q LK LK LK LK K K K L L L L KHz (b).0 KHz 0.9 KHz (d) 0.77 KHz.. One perid (0,T) each f w peridic wavefrms, W and W are shwn in Fig.P.. The magniudes f he n h Furier series cefficiens f W and W, fr n, n dd, are respecively prprinal n 3 and n (b) n n 3 and n and n 0 W T/ T 0 T/ W T (d) n 4 and n.3. Le u() be he sep funcin. Which f he wavefrms in Fig.P.3 (d) crrespnds he cnvluin f u() u( ) wih u() u( )? (b) 0 0 3

8 .5 (d) In Fig.P.4, he seady sae upu vlage crrespnding he inpu vlage 3 4 sin 00 V is 4 π 3 sin 00 V 4 π (b) 3 4 sin 00 V π sin 00 V 4 π (d) 3 4 sin 00 V 4 KΩ inpu 0µF upu.5. In a digial cmmunicain sysem emplying Frequency Shif Keying (FSK), he 0 and bi are represened by sine waves f 0 KHz and 5 KHz respecively. These wavefrms will be rhgnal fr a bi inerval f 45 µsec (b) 00 µsec 50 µsec (d) 50 µsec.6. A message m() bandlimied he frequency f m has a pwer f P m. The pwer f he upu signal in he Fig.P.6 is (b) (d) P csθ m P m 4 P sin θ m Pm 4 cs 4 θ m()csω (muliply) cs(ω θ) Ideal lw pass filer cu ff F=f m pass band gain = Oupu signal (ω >πf m).7. The Hilber ransfrm f cs ω sinω is sinω csω (b) sinω cs ω csω sinω (d) sinω sinω

9 .8. A sysem has a phase respnse given by φ(ω), where ω is he angular frequency. The phase delay and grup delay a ω = ω are respecively given by φ ( ω ) dφ ( ω ), (b) φ ( ω ) ω ω ( ) φ ω, dω ω = ω ( ) d φ ω, dω dφ ( ω ) ω (d) ( ), ( ) dω ω = ω ω = ω ω φ ω φ λ dλ.9. A sysem described by he ransfer funcin is sable. The cnsrains n α and k are. s αs ks 3 ( ) = 3 H s α > 0, αk < 3 (b) α > 0, αk > 3 α > 0, αk > 0 (d) α > 0, αk < 0.0. In an FM sysem, a carrier f 00 MHz is mdulaed by a sinusidal signal f 5 KHz. The bandwidh by arsn s apprximain is MHz. If y() = (mdulaed wavefrm) 3, han by using arsn s apprximain, he bandwidh f y() arund 300 MHz and he and he spacing f specral cmpnens are, respecively. 3 MHz, 5 KHz 3 MHz, 5 KHz (b) MHz, 5 KHz (d) MHz, 5 KHz.. A unifrm plane wave in air impinges a 45 angle n a lssless dielecric maerial wih dielecric cnsan εr. The ransmied wave prpagaes in a 30 direcin wih respec he nrmal. The value f ε r is.5 (b).5 (d).. Fr an 8 fee (.4 m) parablic disk anenna peraing a 4 GHz, he minimum disance required fr far field measuremen is clses 7.5 cm (b) 5 cm 5 m (d) 50 m.3. A recangular wave guide has dimensins cm 0.5 cm. Is cuff frequency is db (b) 5 db 8 db (d) db.4. A recangular wave guide has dimensins cm 0.5 cm. Is cuff frequency is 5 GHz (b) 0 GHz 5 GHz (d) 0 GHz.5. Tw caxial cables and are filled wih differen dielecric cnsans λ εr and εr respecively. The rai f he wavelenghs in he w cables, is λ εr ε r εr (b) ε r ε ε r r εr (d) ε r

10 SETION B (75 marks) This secin cnsiss f TWENTY quesins f FIVE marks each. Aemp ANY FIFTEEN quesins u f hem. If mre number f quesins are aemped, scre ff he answers n be evaluaed, else nly he firs fifeen unscred answers will be cnsidered. 3. Fr he circui in Fig.P3 Find he Thevenin equivalen f he sub circui faced by he capacir acrss he erminals a, b. Ω Ω (b) Find vc ( ), > 0, given vc ( 0) = 0 a Find i ( ), > 0 Ω V F 4V b i() 4. Fr he circui in Fig.P4, which is in seady sae Find he frequency ω a which he magniude f he impedance acrss erminals a, b reaches a maximum. (b) Find he impedance acrss a, b a he frequency ω If v ( ) = V ( ω ) i ( ) i ( ) 5. Fr he circui in Fig.P5, wrie he sae equains using v and il as sae variables. V Ω Fig.P3 s sin, find L,. Ω a Ω 4F V i() ~ i L i b c V V F Ω ε v i L H 6. The newrk N in Fig.P6 cnsiss nly f w elemens: a resisr f Ω and an inducr f L Henry. A 5 V surce is cnneced a he inpu a = 0 secnds. The inducr curren is zer a =0. The upu vlage is fund be 5 e V, fr Find he vlage ransfer funcin f he newrk. (b) Find L, and draw he cnfigurain f he newrk. Find he impulse respnse f he newrk. 3 Inpu vlage N Oupu vlage

11 7. Fr he linear, ime invarian sysem whse blck diagram is shwn in Fig.P7, wih inpu x() and upu y(), Find he ransfer funcin. (b) Fr he sep respnse f he sysem [i.e. find y() when x() is a uni sep funcin and he iniial cndiins are zer] Find y(), if x() is as shwn in Fig.P7(b), and he iniial cndiins are zer. x() x() Σ y() 4 3 Fig.P7 Fig.P7(b) 8. A cerain linear, imeinvarian sysem has he sae and upu represenain shwn belw: x& x = u x & 0 3 x 0 x y = ( ) x Find he eigen values (naural frequencies) f he sysem. (b) If u() = δ() and x ( ) x ( ) x ( ) x ( ) y ( ) 0 = 0 = 0, find, and, fr > 0. When he inpu is zer, chse iniial cndiins ( ) ( ) ( ) x 0 and x 0 such ha y = Ae fr > The blck diagram f a feedback sysem is shwn in Fig.P9. Find he clsed lp ransfer funcin. (b) Find he minimum value f G fr which he sep respnse f he sysem wuld exhibi an versh, as shwn in Fig.P9(b). Fr G equal wice his minimum value, find he ime perid T indicaed in Fig.P9(b). V () Inpu Σ G s s ( 5) (G>0) Oupu (V S) Sep respnse

12 0. Fr Fig.P0, Pl v under seady sae cndiins, wih and wihu. Assume ha he dide is ideal. (b) Design a circui using w ideal dides, ne resisr and w vlage surces ha wuld cnver he inpu vlage f Fig.P0(b) he upu vlage f Fig.P0. The resisr value need n be specified. V i v i v Fig.P0 V i V i 0V 0 5V 0V 5V Fig.P0(b) Fig.P0. Fr he amplifier f Fig.P, T I =.3 ma, = kω, E = 500 Ω, VT = = 6 mv, β = 00, V = 5V q ( ) ν = 0.0 sin ω V and = = 0 µ F. s b e ν Wha is he smallsignal vlage gain, A ν =? ν (b) Wha is he apprximae Wha will ν be if b Aν if e is remved? is shrcircuied? s b V I V V S ~ E E. Fr a feedback amplifier, he pen lp ransfer funcin has hree ples a 00k rad/s, M rad/s and 0 M rad/s. The lw frequency pen lp gain is 000 and he feedback facr (β) is. Use Bde pls deermine he phase margin f he amplifier. Is he amplifier sable?

13 3. Fig.P3 shws a cmmn base amplifier. Wrie expressins fr he imecnsans assciaed wih he capacirs, and. B S (b) Wha is he apprximae lwer cuff frequency f he amplifier? V V s B s E ~ V s 4. Fr he MOS mnsable mulivibrar f Fig.P4, = 50 kw, = 0.0µF, V = 5 V, and he MOS NO gaes have a hreshld vlage ( VT ) f.5 V. ν in is a DD rigger pulse ( τp ) as shwn in he figure. Pl ν 0 and ν as funcins f ime. (b) Wrie he equain fr ν ( ), fr > 0. Find he ime perid f he upu pulse. V in V in V 0 V 0 5V 0 τ P V 5. The peraing cndiins (ON =, OFF = 0) f hree pumps (x,y,z) are be mnired. x = implies ha pump X is n. I is required ha he indicar (LED) n he panel shuld glw when a majriy f he pumps fail. Ener he lgical values in he Kmap in he frma shwn in Fig.5. derive he minimal Blean sum f prducs expressin whse upu is zer when a majriy f he pumps fail. (b) The abve expressin is implemened using lgic gaes, and pin P is he upu f his circui, as shwn in Fig.P5(b). P is a 0 V when a majriy f he pumps fails and is a 5 V herwise. Design a circui drive he LED using his upu. The curren hrugh he LED shuld be 0 ma and he

14 vlage drp acrss i is V. Assume ha P can surce r sink 0 ma and a 5 V supply is available. xy xy xy xy z z Lgic ircui P 6. A nebi full adder is be implemened using 8 muliplexers (MUX). Wrie he ruh able fr sum (S) and carry he nex sage ( N ) in erms f he w bis (A, B) and carry frm he previus sage ( p ). The ruh able shuld be in he ascending rder f (A,B, p), i.e. (000,00,00, ec.). (b) Implemen S and N using 8 muliplexers. 7. The prgram and machine cde fr an 8085 micrprcessr are given by 3E MVI A NOP 80 ADD B 3D DE A JNZ 800A 0A 80 3 JMP D3 OUT HLT The saring address f he abve prgram is 7FFF H. Wha wuld happen if i is execued frm 8000 H? (b) Fr he insrucins given belw, hw many memry perains (read/wrie) are perfrmed during he execuin in an 8085 µp? Wrie an insrucin which akes he minimum pssible ime clear he accumular f he 8085.

15 8. A band limied signal x() wih a specrum X(f) as shwn in Fig.P8 is prcessed as shwn in Fig.P8(b). p() is a peridic rain f impulses as in Fig.P8. The ideal bandpass filer has a passband frm 6 KHz 34 KHz. alculae he Furier series cefficiens n in he Furier expansin f p() in he frm p ( ) jnπ = ex n p T n= (b) Find he Furier Transfrm f p(). Obain and skech he specrum f xs ( ). (d) Obain and skech he specrum f y ( ). x(f) x() x S() Ideal band pass filer 0 4KHz f in KHz p() y() Fig.P8 Fig.P8(b) Train f impulses f uni srengh T 0 T T 3T Time 0KHz T = T Fig.P8 9. Zer mean whie Gaussian nise wih a wsided pwer specral densiy f 4 W/Khz is passed hrugh an ideal lwpass filer wih a cuff frequency f KHz and a pass band gain f, prduce he nise upu n(). Obain he al pwer in n(). (b) Find he aucrrelain funcin E[n()n(τ) f he nise n() as a funcin f τ. Tw nise samples are aken a imes and. Find he spacing s ha he prduc n ( ) n ( ) has he ms negaive expeced value and bain his ms negaive expeced value.

16 0. Given ( 4 0 j x E = e k ) yv ˆ min free space. Wrie all he fur Maxwell s equains in free space. (b) Find E. Find H.. The hree regins shwn in Fig.P are all lssless and nnmagneic. Find Wave impedance in mediums and 3. (b) d such ha medium acs as a quarer wave λ 4 ransfrmer. eflecin cefficien ( Γ) and vlage sanding wave rai (VSW) a he inerface f he medium and, when d = λ 4 Medium ε r= Inciden Team Wave (f=ghz) Medium ε r=5 d Medium 3 ε r3=9. Design a lssless impedance maching newrk shwn in Fig.P ransfrm Z = 0 j0ω Z = 50 Ω. Find he values f L, and qualiy facr (Q) f he L circui a f = GHz. in L Z in Z L