EE215ClassProblems,Week6
Solutions
Allquestionsareinitiallylistedinblack.Afterclass,thosethatwerecoveredinclassusingTopHat
(asclassactivities)willbehighlightedinblue.Questionsremaininginblack(afterclass)maybe
usedforadditionalreview.Solutionsarenotedinitalics.
Week6,Q1
Inthefollowingopampcircuit
Vouthastheform:
Vout=K1+K2Vin
whereK1isaconstantandK2isthegainoftheamplifier.
Usetheidealopammodelinyouranalysis.
PartAandB:
WhatareK1andK2ifVref=0?
Solution:
Thisisasimpleinvertingamplifier,so:
Vout=-60k/10kVin=-6Vin
K1=0;andK2=-6
PartCandD:
WhatareK1andK2ifVref=5?
Solution:
Bytheidealopampmodel:
v+=v-=5Volts
Nodalanalysisattheminusnodegives:
(Vin-5)/10k=(5-Vout)/60k
Vin/10k-5/10k=-Vout/60k
Vout=35-6Vin
K1=35;andK2=-6
PartE
SketchVoutforbothlinearandsaturatedoperation(Vinrangingfrom-10to+10V)ineachofParts
AandBandPartsCandD.Whatdoyouseeinthedifferencebetweenthetwoamplifiers?
15
10
5
Vout(PartAandB)
0
-15
-10
-5
0
5
10
15
Vout(PartCandD)
-5
-10
-15
Solution:
Thesecondamplifiershiftsthegaincurvetotheright(ifweignoredsaturationoftheamplifier,the
outputvoltagewouldbe/isoffsetby35V).
PartF
WhatwouldthevalueofVrefhavetobesothatthecurveinPartEwasoffsetby+5V?
Solution:
Thedesiredexpressionis:
Vout=5-6Vin
Usingnodalanalysisagaingives:
(Vin-Vref)/10k=(Vref-Vout)/60k
Solving:
Vref=0.71V
PartG
Sketchthethreescenarios(PartA/B,PartC/D,andPartF)
15
10
5
-5
-3
0
-1
-5
Vout(PartAandB)
Vout(PartCandD)
1
3
5
7
9
11
Vout(PartE)
-10
-15
Week6,Q2
Inthefollowingopampcircuit,findtheoutputvoltagevoandtheoutputcurrentio.Usetheideal
opampmodeltoanalyzethecircuit.
Solution:
Byobservation:
v+=0
Bytheidealopampmodel:
v-=v+=0
Bynodalanalysis:
(0.150-0)/2000=(0-v1)/40k
Solving:
v1=-3V
Bynodalanalysis:
(0-v1)/40k=v1/20k+(v1-vo)/50k
Solving:
vo=-14.3V
Bynodalanalysis:
io+vo/25k=(v1-vo)/50k
io=0.792mAor0.8mA
Week6,Q3
Atwhatvalueofinputvoltage(s)doestheopampinthepreviousquestionsaturate?
Solution:
vosaturatesat+15and-15V(idealopampmodel)
Bynodalanalysis:
(0-v1)/40k=v1/20k+(v1-vo)/50k
(0-v1)/40k=v1/20k+(v1-15)/50k
(0-v1)/40k=v1/20k+(v1--15)/50k
Solvingforv1gives:
v1=3.16V
v1=-3.16V
Bynodalanalysis:
(vin-0)/2000=(0-v1)/40k
vin=158mV
vin=-158mV
Week6,Q4
Inthefollowingopampcircuit,whatistheresistanceseen"looking"intothe+andthe-terminals
oftheopamp.Usetheidealopampmodelandde-activatetheoutputvoltagetocalculatetheinput
resistance.
Solution:
Intheidealopampmodel,theresistanceseenlookingintothe+terminalisinfinity(theresistance
between+and-terminalsisinfiniteandthatisallthatisconnectedatthe+terminal.
Atthe-terminal,theresistanceseenlookingintotheterminalis:
Theequivalentresistanceis:
(50k||20k)+40k+2k=56kOhms