EG1108ElectricalEngineering~AdditionalProblemsforPart2

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1. Therectifiersupplyshowninthefigurebelowisusedaspartofanelectronicdevice.The

inputisanACvoltagesourcewithafrequencyof50Hzandapeakamplitudeof200V.The

transformerprimarytosecondaryratio=2:1.Theloadresistanceis100Ω.

(a) Determine the output DC voltage. What is the peak‐to‐peak ripple in the output

voltage?Whatisthepercentageripple?

(b) Sketchwaveformsforvsandvo,respectively.

(c) Suggestanadditionalcomponenttobeaddedtotheabovecircuit,whichcanyielda

smoothertheoutputvoltage.Drawtherevisedcircuit.

2. Considerthetransformercircuitshowninthefigurebelow.Thetransformerturnsratiois

1:2.Theinputtothecircuitisthevoltagesource,vs(t).Determinetheoutputvoltage,vo(t),

acrossthe2Hinductor.

3. ADCpowersupplyconsistsofatransformerfeedingahalf‐waverectifiertogetherwitha

capacitorfilter.ItsuppliesaDCcurrentof1Aat20VDCtoanelectronicequipment.The

ACinputsourceis230V(rms)at50Hz.Thefiltercapacitorhasacapacitanceof60,000μF.

a) Drawthecircuitdiagramofthesupplyarrangement.

b) Determineasuitablewindingratioforthetransformer.

c) Determinethemagnitudeofthepeak‐to‐peakrippleintheoutputvoltage.

2

EG1108ElectricalEngineering~AdditionalProblemsforPart2

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4. Showninthefigurebelowaretheexpressionsoftheprimaryandsecondaryvoltagesofan

ideal transformer. Assume that the transformer reluctance 25 , the numbers of the

turnsoftheprimaryandsecondarywindingsare1 210, 5N N ,respectively.

(a) Giventhewaveformsofi1(t)andi2(t)asthefigurebelow,

sketchthewaveformsoftheinducedvoltages,v1(t)andv2(t).

5. Asoundsystemwithaloudspeakercanberepresentedinacircuitdiagrambelow.Assume

thattheinternalresistanceofthesourceis0.5,andtheresistanceoftheloadis8.

Mi1(t) i2 (t)

2

Ldd ti1(t)

v2(t) 2Mdd ti2(t)

Ldd ti1(t)

v1(t) 1 M dd ti2(t) L1 L2

L1N1 ,

2

L2N2 , M 2 L1 L2 for no flux leakage and perfect coupling

i1(t)

i2(t)

1A

1A

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(a) Findanappropriatetransformerturnsratio,whichresultsinimpedancematching.

(b) Given ( ) 230 2 cos( )sv t t Vandwiththetransformerturningratioobtained in

(a),findtheaveragepowersconsumedbytheloadandbytheinternalresistor.

(c) Given ( ) 230sv t V and againwith the transformer turning ratio obtained in (a),

findtheactualpowersconsumedbytheloadandbytheinternalresistor.

(d) Forboth(b)and(c),determinethepowerconsumedbythetransformer.

6. SuggestaDCpowersupplycircuitthatcanbeusedtostepdowntheelectricsourcefrom

themains(230VAC)topowerupyourlaptop,whichtakes5VDC.Drawthecircuitwith

necessarycomponents.Willyouuseyourdesignforyourownlaptop?Whyorwhynot?

7. ForACenvironments,showthattheprimaryandsecondaryvoltages inthephasor form

aregivenasthoseinthefigurebelow.

Hint:Assume 1 1 1( ) 2 cosi t r t and 2 2 2( ) 2 cosi t r t .

8. ThetransformerisconnectedtoaloadinductorwithinductanceL=2H,asshowninthe

figurebelow.Recallthatthetransformerreluctance 25 , thenumbersoftheturnsof

theprimaryandsecondarywindingsare1 210, 5N N ,respectively.Determinetheratio

oftheprimaryandsecondarycurrents(inphasor).

Whyistheusualtransformerpropertybelownolongervalidinsuchasituation?

1 2

2 1

I N

I N

I1

M

L1 L2

I2

1V L1j I1 j I2M 2V L2j I1 j I2M

EG1108ElectricalEngineering~AdditionalProblemsforPart2

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9 Showninthefigurebelowaretheexpressionsoftheprimaryandsecondaryvoltagesofan

idealtransformerinthephasorforminACenvironments.

Theprimaryandsecondaryinductancesofthetransformerarerespectivelygivenby

2 21 2

1 2 1 2, ,N N

L L M L L

where is the reluctance of the transformer. Let1,peakV and

2,peakV are respectively the

peakvaluesoftheprimaryandsecondaryvoltagesofthetransformer.Showthat

2,peak 2

1,peak 1

V N

V N

10. Thefollowingtransmissionsystemisusedtotransmitelectricpowerfromthesourceto

anACdevice.

Determine the average power lost on the transmission line and the average power

consumedbytheload.Whatisthepowerefficiency?

11. FindI1andI2inthecircuitbelow.

I1

M

L1 L2

I2

1V L1j I1 j I2M 2V L2j I1 j I2M

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12. Findallvoltagesandcurrentsinthecircuitbelow.

13. FindV0inthecircuitbelow.

14. FindV0inthecircuitbelow.

15. Theoutputstageofanamplifieristobematchedtotheimpedanceofaspeakerasshowin

thefigurebelow.Iftheimpedanceofthespeakeris8andtheamplifierrequiresaload

impedanceof3.2k,determinetheturnsratiooftheidealtransformer.

16. Thewaveformshownbelowisappliedasaninputtothehalf‐waverectifiercircuitbelow.

(a)Plottheoutputwaveform,vo(t).(b)Whatisthedcvoltageoutput?

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17. Shownbelow is a half‐wave rectifier circuitwith a filter. Plot the outputwaveformand

estimatethepeak‐to‐peakrippleforC=150F.

18. Anelectroniccalculatoroperatesonadcsupplyof6V.Thissupplyisobtainedfromahalf‐

waverectifierwitha filter. If thecalculatorcanbemodeledasa10k resistanceandit

cantolerateamaximumpeak‐to‐peakvariationof0.1Varoundthedcvalue,calculatethe

minimumvalueofcapacitorthatcanbeusedinthefilter.Assumeacinputis50Hz.

19. Shownbelowisafour‐diodefull‐waverectifiercircuit.(a)Plottheoutputvoltagevo(t).(b)

Determinethemaximumreversevoltageonanydiode.(c)Whatisthedcoutputvoltage?

20. Shownbelowisatwo‐diodefull‐waverectifiercircuit.Plottheoutputvoltagewaveform,

andestimatethepeak‐to‐peakripple.Determinethemaximumreversevoltageoneither

diode.

21. AmajoritydetectorhasthreeinputvariablesA,BandCandtwooutput light indicators.

Greenlight(G)willbeonifmajorityoftheinputvariablesareequalto1.Redlight(R)will

beonifmajorityoftheinputvariablesareequalto0.

(a) Constructatruthtableforyourdesign.

(b) ObtainlogicalexpressionsforGandR,respectively.

(c) DrawlogiccircuitimplementationsforGandR.

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22. ProvethefollowingDeMorgan’slaw:

A B C A B C

23. Use theDeMorgan’s lawsandanyof first17 rulesofBooleanAlgebra toprove the last

rule,i.e.,Rule18:

A A B A B

24. Consideralogicalexpression

( ) ( )W A C B C

a) ConstructatruthtableforW.

b) UsetheKarnaughmaptechniquetosimplythelogicalexpression.

c) Implementthelogicalexpressionobtainedin(ii)usingonly2two‐inputNORgates.

25. AnLEDdisplaypanelshowninthefigurebelowhasfourLEDlightbarslabeledA,B,Cand

D, respectively.Youare required todesignanappropriatedigital logic circuit todisplay

LettersFandLusingthepanel.

(a) Constructatruthtableforyourdesign.

(b) ObtainlogicalexpressionsforFandL,respectively.

(c) Draw logic circuit implementations forF andLusingonly2‐inputNORgates (i.e.,

eachNORgateonlyhastwoinputchannels).Foreachletter,youcannotusemore

than8NORgatesfortheimplementation.

(d) WhatotherEnglishletterscanbedisplayedbythepanel?

26. Derivealogicalexpressionfortheswitchcircuitshowninfigurebelow.

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27. ThetruthtablebelowshowstherelationshipbetweeninputsA,B,CandD,andoutputZ.

(a) FindZintermsofA,B,CandDintheSum‐of‐products(SOP)form.

(b) SimplytheexpressionobtainedusingKarnaughmap.

(c) Implement the logicalexpressionobtained in (b)usingnomore than4 two‐input

NORgates(i.e.,eachNORgateonlyhastwoinputchannels).

28. Amultiplexer is a device setting its single output to the same value as one of itsmany

inputs. Shown in the figurebelow is amultiplexerof two inputs, X andY, inwhichX is

selectedwhenthecontrolinputC=0andYisselectedwhenC=1.

(a) AssumethatbothXandYarelogicalvariables,constructatruthtablefortheabove

multiplexer.

(b) ObtainalogicalexpressionforZintheSOPform.

(c) UseKarnaughmaptosimplifytheexpressionofZobtainedinPart(b).

(d) Draw a logic circuit implementation for Zusing no more than 7 two‐input NOR

gates(i.e.,eachNORgateonlyhastwoinputchannels).

29. PrepareatruthtableforeachofthefollowingBooleanexpressions:

(a) F A B A B

(b) F A B C A B C A B C

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30. WithoutusingKmaps,simplythefollowingBooleanexpressions:

(a) F A C C D B C D

(b) F A B C B C A B D B C D

31. UsingKmaps,simplytheBooleanexpressionsinProblem30.

32. DerivetheBooleanexpressionsforthelogiccircuitsshownbelow.

33. DrawthelogicdiagramforthefollowingBooleanexpressions,withoutsimplifications:

(a) F A B B C A B D A C D

(b) ( ) ( ) ( )F X Y X Z Y Z

(c) F A C B C A B C

(d) ( ) ( ) ( )F X Y X Z Y Z

34. RepeatProblem33withsimplification.

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35. DerivetheBooleanexpressionsforthelogiccircuitsbelow.

36. Thelogiccircuitbelowisknownasaparitycheckerfora4‐bitbinarynumber.(a)Derive

itsBooleanexpression.(b)Prepareitstruthtable.(c)Canyourealizethesamefunctionby

usingfewerlogicgates?

37. Thelogiccircuitshownbelowisonepartofthemagnitudecomparatorusedtocompare

twobinarynumbers.(a)Prepareitstruthtable.(b)Canyoudescribethiscircuit?