EG1108PART 2 EXERCISES ~PAGE 1EG1108PART 2 EXERCISES ~PAGE 1 BEN M.CHEN,NUSECEBEN M.CHEN,NUSECE

EG1108Tutorial5:Transformers&RectifierCircuits– Part1EG1108Tutorial5:Transformers&RectifierCircuits– Part1

1. Itisshowninthelecturethatanidealmutualinductorhasthefollowingproperties:

ShowintheACenvironment,thepropertiescanberepresentinfollowingphasor form:

EG1108PART 2 EXERCISES ~PAGE 2EG1108PART 2 EXERCISES ~PAGE 2 BEN M.CHEN,NUSECEBEN M.CHEN,NUSECE

2. Anidealtransformerhasaturnsratioof3:2.Itisdesiredtooperatea200 resistiveloadat150V.Findtheprimaryandsecondarycurrents,thesourcevoltage,thepowerdeliveredtotheprimaryfromthesource,andtheimpedancethesourceseeslookingintotheprimarywinding.

Answers:0.5 A,0.75 A,225 V,112.5 W,450

3. Atransformeristobeusedtomatchan8 loudspeakertoa500 audioline.Theaudiopowerdeliveredtothespeakeris10W.Find:

i. turnsratioofthetransformer,

ii. thevoltagesatprimaryandsecondaryterminalsofthetransformer.

Assumethatthespeakerisresistiveandthatthetransformerisideal.

Answers:turnsratio=7.9:1;V2=8.94V,V1=70.6V

4. Thehighvoltagesideofastep‐downtransformerhas800turns,andthelowvoltagesidehas100turns.Avoltageof2400 Visappliedtothehighvoltagesideanda3+j4Ωloadisconnectedonthelowvoltageside.Find:

i. Thesecondaryvoltageandcurrent.

ii. Theprimarycurrent.

iii. Thereflectedimpedanceseenfromtheprimaryside.

Answers:300 V, 6 53.13 A; 0.75 53.13 A; 320 53.13 Ω

EG1108Tutorial5(cont.)EG1108Tutorial5(cont.)

EG1108PART 2 EXERCISES ~PAGE 3EG1108PART 2 EXERCISES ~PAGE 3 BEN M.CHEN,NUSECEBEN M.CHEN,NUSECE

5. Considerthetransformercircuitasshownbelow.Theinputtothecircuitisthevoltageofthevoltagesource,vs(t).Determinetheoutputvoltage,vo(t)acrossthe6Hinductor.Thetransformationratiois2:5.

Answer:

s ( )8.92cos(2 74 ) Vv t

t

o ( ) 4.684cos(2 151.85 ) Vv t t

EG1108Tutorial5(cont.)EG1108Tutorial5(cont.)

EG1108PART 2 EXERCISES ~PAGE 4EG1108PART 2 EXERCISES ~PAGE 4 BEN M.CHEN,NUSECEBEN M.CHEN,NUSECE

1. i.AvoltagesourceVS isconnectedtoaresistiveloadRL =10ΩbyatransmissionlinehavingaresistanceRline =10Ω,asshowninFigureQ1.1.Determinethepowerdeliveredbythesource,powerlostinthelineresistance,powerdeliveredtotheloadandtheefficiency(expressedasthepowerdeliveredtotheloadasapercentageofpowersuppliedbythesource).

ii.Thispowertransmissionsystemisnowmodifiedtoincludetwotransformers.Atransformerofturnsratio1:10isusedtostepupthesourcevoltageatoneendofthetransmissionline(sendingend),andanothertransformerofturnsratio10:1isusedtostepdownthevoltageto100Vattheload(receivingend)asshowninFigureQ1.2.Calculatethepowerdeliveredbythesource,powerlostinthelineresistance,powerdeliveredtotheloadandtheefficiencyinthiscase,andcomparewiththevaluesobtainedin(i)above.Whatconclusionscanyoudrawfromthis?

Answers:i.Efficiency=50%;ii.Efficiency=99.01%

FigureQ1.1

FigureQ1.2

EG1108Tutorial6:Transformers&RectifierCircuits– Part2EG1108Tutorial6:Transformers&RectifierCircuits– Part2

EG1108PART 2 EXERCISES ~PAGE 5EG1108PART 2 EXERCISES ~PAGE 5 BEN M.CHEN,NUSECEBEN M.CHEN,NUSECE

3. Afullwavebridgerectifier,withalargesmoothingcapacitorissupplyingpowertoa10Ωloadresistance.Thesecondaryvoltageofthetransformersupplyingpowertherectifieris8V(rms)at50Hz.Assumingthatthediodesareideal,whatistheapproximatevalueoffiltercapacitorrequiredsuchthatthepeak‐to‐peakrippleis5%orless?

Answer:0.02F

2. ADCpowersupplyconsistsofatransformerfeedingahalf‐waverectifiertogetherwithacapacitorfilter.ItsuppliesaDCcurrentof1Aat12VDCtoanelectronicequipment.TheACinputsourceis230V(rms)at50Hz.Theoutputsidefiltercapacitorusedis50000μF.

i. Drawthecircuitdiagramofthesupplyarrangement.

ii. Determineasuitablewindingratioforthetransformer.Treattheoperationofthepowersupplyasideal(i.e.,neglectvoltagedropinthediodeandassumethatthetransformerisideal).

iii. Whatisthepeak‐to‐peakrippleintheoutputvoltage?Whatistheripplefrequency?Whatisthepercentageripple?

iv. Sketchthefollowingwaveforms:ACinputvoltage,secondaryACvoltage,rectifieroutputvoltage.Marktheintervalwhenthediodeconducts.

Answers:(ii)27:1;(iii)%ripple=3.33%

EG1108Tutorial6(cont.)EG1108Tutorial6(cont.)

EG1108PART 2 EXERCISES ~PAGE 6EG1108PART 2 EXERCISES ~PAGE 6 BEN M.CHEN,NUSECEBEN M.CHEN,NUSECE

4. TherectifiersupplyshowninFigureQ4isusedaspartofanelectroniccircuit.Theinputvoltageissinusoidalwithapeakamplitudeof50V,and10kHzfrequency.Thetransformerprimarytosecondaryratio=1:3.Theloadresistanceis10kΩ. Neglectdiodeconductionvoltagedrops.Also,assumeidealoperationofthetransformerneglectingleakage,lossesetc.

i. DeterminetheoutputDCvoltage.Whatisthepeak‐to‐peakrippleintheoutputvoltage?Whatisthepercentageripple?

ii. Sketchwaveformsforv1 ,v2,v3 ,vYX,vo,io ,i2,i3,vD2.Markthediodeconductionintervals.

iii. Whatisthemaximumreversevoltageappliedacrossthediodes?Whendotheyoccur?

Answers: i.47.8V;75V;157%;iii.150V

FigureQ4

EG1108Tutorial6(cont.)EG1108Tutorial6(cont.)

EG1108PART 2 EXERCISES ~PAGE 7EG1108PART 2 EXERCISES ~PAGE 7 BEN M.CHEN,NUSECEBEN M.CHEN,NUSECE

5. Forthehalf‐waveandfull‐waverectifiercircuitswithcapacitorfilteringthatwehavestudied,commentwhethertheresultingoutputvoltagewillbesmoothDCiftheinputvoltageisgivenasfollows.

Giveyourjustification.

Answers: Yesifthecapacitanceissufficientlylarge

EG1108Tutorial6(cont.)EG1108Tutorial6(cont.)

2Vm

Vm

EG1108PART 2 EXERCISES ~PAGE 8EG1108PART 2 EXERCISES ~PAGE 8 BEN M.CHEN,NUSECEBEN M.CHEN,NUSECE

EG1108Tutorial7:DigitalLogicCircuits– Part1EG1108Tutorial7:DigitalLogicCircuits– Part1

1. SimplifythefollowingBooleanexpressionsusingrulesofBooleanAlgebraandDeMorgan’stheorems:

i. Answer:

ii. Answer:

iii. Answer:

iv. Answer:

v. Answer:

2. DerivetheBooleanfunctionsforthecombinatorialnetworkshowninfiguresbelow.

i) ii)

Answers:

( ) ( )F A B A B

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

F A

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

F A B A B B C F B C

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

Z A B A C B C 4 ( ) ( )F X Y Z Y X Y

EG1108PART 2 EXERCISES ~PAGE 9EG1108PART 2 EXERCISES ~PAGE 9 BEN M.CHEN,NUSECEBEN M.CHEN,NUSECE

3. UseonlyNORgateswith2inputstofindawaytoimplementtheexclusiveORfunction .

EG1108Tutorial7(cont.)EG1108Tutorial7(cont.)

Z A B

5. Thelogiccircuitbelowisknownasaparitycheckerfora4‐bitbinarynumber.

i. Constructatruthtableforthecircuit.

ii. VerifythatFistrueifandonlyifthenumberoftheinputsthatarehighiseither1or3.

4. UseonlyNANDgateswith2inputstofindawaytoimplementtheexclusiveNORfunction . Z A B

EG1108PART 2 EXERCISES ~PAGE 10EG1108PART 2 EXERCISES ~PAGE 10 BEN M.CHEN,NUSECEBEN M.CHEN,NUSECE

EG1108Tutorial8:DigitalLogicCircuits– Part2EG1108Tutorial8:DigitalLogicCircuits– Part2

1. ThetruthtablebelowshowstherelationshipbetweeninputsA,BandC,andtheoutputZ.

i. FindZintermsofA,BandCusingSum‐Of‐Products(SOP)form.

ii. FindZintermsofA,BandCusingProduct‐Of‐Sums(POS)form.

Answers: SOP:

POS:

A B C Z0 0 0 10 0 1 10 1 0 00 1 1 11 0 0 01 0 1 11 1 0 01 1 1 0

Z A B C A B C A B C A B C

Z A B C A B C A B C A B C

2. A Boolean expression is given below:

i. UserulesofBooleanAlgebratosimplifythisBooleanfunction.

ii. UseKarnaugh maptosimplifytheBooleanfunction. Answer:

F A B C A B C D A C D A B C D A B C D

F B C A D

EG1108PART 2 EXERCISES ~PAGE 11EG1108PART 2 EXERCISES ~PAGE 11 BEN M.CHEN,NUSECEBEN M.CHEN,NUSECE

4. Fromthetableshownbelow,findZintermsofA,BandCusingProduct‐Of‐Sums(POS)form.UseKarnaugh maptosimplifytheresultingexpression.

Answer:

A B C Z0 0 0 10 0 1 00 1 0 00 1 1 11 0 0 01 0 1 11 1 0 01 1 1 0

( ) ( ) ( ) ( )Z A B B C A C A B C

3. UseKarnaugh maptosimplifythefollowingBooleanfunction:

Answer:F A B C A B C A C A B D B C F C A B B D

EG1108Tutorial8 (cont.)EG1108Tutorial8 (cont.)

EG1108PART 2 EXERCISES ~PAGE 12EG1108PART 2 EXERCISES ~PAGE 12 BEN M.CHEN,NUSECEBEN M.CHEN,NUSECE

EG1108Tutorial8 (cont.)EG1108Tutorial8 (cont.)

5. Designalogiccircuittocontrolelectricalpowertotheengineignitionofaspeedboat.

LogicoutputIistobecomehighifignitionpoweristobeappliedandremainlow otherwise.Gasolinefumesintheenginecompartmentpresentaserioushazardofexplosion.AsensorprovidesalogicinputFthatishighiffumesarepresent.Ignitionpower shouldnotbeappliediffumesarepresent.Tohelppreventaccidents,ignitionpowershouldnotbeappliedwhiletheoutdriveisingear.LogicsignalGishighiftheoutdriveisingearandislowotherwise.

Ablowerisprovidedtoclearfumesfromtheenginecompartmentandistobeoperatedforfiveminutesbeforeapplyingignitionpower.LogicsignalBbecomeshighaftertheblowerhasbeeninoperationforfiveminutes.Finally,anemergencyoverridesignalEisprovidedsothattheoperatorcanchoosetoapplyignitionpowereveniftheblowerhasnotoperatedforfiveminutesandiftheoutdriveisingear,butnotifgasolinefumesarepresent.

i. PrepareatruthtablelistingallcombinationsoftheinputsignalsB,E,Fand G.AlsoshowthedesiredoutputIforeachrowinthetable.

ii. Usingthesum‐of‐productsapproach,writeaBooleanexpressionforI.

iii. MinimizethisexpressionusingKarnaugh map.Answer:

iv. Implementthelogiccircuitwiththeleastnumberofgates(youcanassumethatAND,ORandNOTgatesareavailable).

I = E F + B F G