双语建模实验⑦及答案.docx
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双语建模实验⑦及答案.docx
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双语建模实验⑦及答案
EXAMPLE7
Step-down(BUCK)dc-dcConverter
1,Insteadystate,obtainthefollowingwaveformsusingBuckconv:
(a)vLandiLwaveforms.
(b)vo,iLandicwaveforms
Answer:
(a)thevLwaveform:
iLwaveform:
(b)
vowaveform:
iLwaveform:
Icwaveform:
2,ObtainvoiwaveformandbymeansofFourieranalysis,obtainitsharmoniccomponents
asaratioofitsaveragevalueVo.
Answer:
Voiwaveform:
FOURIERCOMPONENTSOFTRANSIENTRESPONSEV(n00037,0)
DCCOMPONENT=5.821027E+00
HARMONICFREQUENCYFOURIERNORMALIZEDPHASENORMALIZED
NO(HZ)COMPONENTCOMPONENT(DEG)PHASE(DEG)
11.000E+053.924E+001.000E+00-4.431E+010.000E+00
22.000E+052.829E+007.210E-011.337E+008.995E+01
33.000E+051.412E+003.598E-014.690E+011.798E+02
44.000E+051.131E-012.883E-029.031E+012.675E+02
55.000E+057.158E-011.824E-01-4.135E+011.802E+02
66.000E+059.350E-012.383E-013.981E+002.698E+02
77.000E+056.445E-011.642E-014.910E+013.592E+02
88.000E+051.131E-012.882E-029.015E+014.446E+02
99.000E+053.560E-019.073E-02-3.763E+013.611E+02
101.000E+065.514E-011.405E-016.751E+004.498E+02
111.100E+064.319E-011.101E-015.111E+015.385E+02
121.200E+061.131E-012.882E-029.010E+016.218E+02
131.300E+062.157E-015.496E-02-3.277E+015.432E+02
141.400E+063.836E-019.777E-029.724E+006.300E+02
151.500E+063.301E-018.412E-025.300E+017.176E+02
161.600E+061.131E-012.882E-029.007E+017.990E+02
171.700E+061.404E-013.579E-02-2.600E+017.272E+02
181.800E+062.878E-017.333E-021.301E+018.105E+02
191.900E+062.690E-016.856E-025.482E+018.966E+02
202.000E+061.131E-012.882E-029.005E+019.762E+02
212.100E+069.410E-022.398E-02-1.592E+019.145E+02
222.200E+062.246E-015.724E-021.676E+019.915E+02
232.300E+062.273E-015.794E-025.664E+011.076E+03
TOTALHARMONICDISTORTION=9.212637E+01PERCENT
JOBCONCLUDED
TOTALJOBTIME.74
TheTOTALHARMONICDISTORTIONis9.212637E+01PERCENT(%THD=0.9212637),
WhileaveragevalueVois5.821027E+00(Vo=5.821027),soharmoniccomponents
asaratioofitsaveragevalueVois0.1583
3,Increasetheloadresistanceto10Ω.ObtainvLandiLwaveformsinthe
discontinuousconductionmode[Hint:
useV(0)=5.8VandIL(0)=0].Checkifthe
resultsagreewiththefollowingequation:
=
whereILB,max=
.Answer:
vLwaveform:
ILwaveform:
(a)
FOURIERCOMPONENTSOFTRANSIENTRESPONSEV(VOUT,0)
DCCOMPONENT=6.894733E+00
(b)FOURIERCOMPONENTSOFTRANSIENTRESPONSEI(R_Rload)
DCCOMPONENT=6.894733E-01
Vo=6.894733E+00,vd=8v,io=6.894733E-01,ILB,max=2A,
Sovo/vd=0.8618,while
=0.8671
4,Obtainthepeak-to-peakrippleintheoutputvoltageandchecktoseeiftheresultsagreewiththeanalyticalcalculations
(1)thepeak-to-peakrippleintheoutputvoltageis5.9614-5.9205=0.0409
(2)FOURIERCOMPONENTSOFTRANSIENTRESPONSEV(VOUT,0)
DCCOMPONENT=5.942967E+00,soVo=5.942967v,Ts=10us
0.03714
5,Calculatethermsvalueofthecurrentthroughtheoutputcapacitorasaratioofthe
averageloadcurrentIo.
FOURIERCOMPONENTSOFTRANSIENTRESPONSEI(C_C1)
DCCOMPONENT=9.237352E-03
HARMONICFREQUENCYFOURIERNORMALIZEDPHASENORMALIZED
NO(HZ)COMPONENTCOMPONENT(DEG)PHASE(DEG)
11.000E+051.026E+001.000E+00-1.351E+020.000E+00
22.000E+053.565E-013.476E-01-9.870E+011.716E+02
33.000E+051.168E-011.139E-01-7.236E+013.331E+02
44.000E+054.192E-024.086E-02-9.561E+014.450E+02
55.000E+054.433E-024.322E-02-1.017E+025.740E+02
66.000E+053.096E-023.018E-02-7.840E+017.325E+02
77.000E+051.245E-021.213E-02-8.482E+018.612E+02
88.000E+051.702E-021.659E-02-1.188E+029.623E+02
99.000E+052.087E-022.035E-02-9.232E+011.124E+03
101.000E+061.552E-021.513E-02-5.502E+011.296E+03
111.100E+064.751E-034.632E-03-3.282E+011.454E+03
121.200E+064.473E-034.361E-03-1.232E+021.498E+03
131.300E+067.165E-036.984E-03-9.747E+011.659E+03
141.400E+065.155E-035.025E-03-7.188E+011.820E+03
151.500E+062.914E-032.841E-03-9.170E+011.935E+03
161.600E+064.323E-034.214E-03-9.960E+012.063E+03
171.700E+064.049E-033.947E-03-7.232E+012.225E+03
181.800E+061.518E-031.480E-03-6.081E+012.372E+03
191.900E+062.459E-032.397E-03-1.364E+022.431E+03
202.000E+064.538E-034.424E-03-1.087E+022.594E+03
212.100E+063.994E-033.894E-03-7.279E+012.765E+03
222.200E+062.042E-031.991E-03-5.193E+012.921E+03
232.300E+061.416E-031.380E-03-9.900E+013.009E+03
TOTALHARMONICDISTORTION=3.734869E+01PERCENT
%THD=
%THD=3.734869E+01PERCENT=0.3734869,Is1=1.026E+00
Is=0.7744A
FOURIERCOMPONENTSOFTRANSIENTRESPONSEI(R_Rload)DCCOMPONENT=1.188629E+01
Io=11.88629/
=8.405
SoIs/Io=0.0921
6.Calculatethepeak-to-peakrippleintheoutputvoltageinthepresenceoftheoutput
capacitorEquivalentSeriesResistance(ESR)[SuggestedESR=100mΩ].Plotthe
rippleacrossC,ESRandthetotalrippleinvo.
Vc1waveform:
Vesrwaveform:
thetotalrippleinvowaveform:
EXAMPLE10
Full-Bridge,Bipolar-Switchingdc-dcConverter
1,ObtainthefollowingwaveformsusingFBBSDCDC:
(a)vo,ioandpo(t)=voio
(b)voandid
Answer:
(1)vowaveform:
Iowaveform:
Po(t)waveform:
(2)vowaveform:
Idwaveform:
2,Calculatepeak-to-peakrippleinio.
FromIowaveform,wecanseethepeaktopeakrippleiniois(155.35-153.32)=2.13A
3,BymeansofFourieranalysis,calculatetheaveragevalueandtheharmoniccomponents
invo.Obtainthermsvalueoftherippleinvoandcheckitwiththeanalytical
calculations.
FOURIERCOMPONENTSOFTRANSIENTRESPONSEV(n00396,n00826)
DCCOMPONENT=7.940968E+01
HARMONICFREQUENCYFOURIERNORMALIZEDPHASENORMALIZED
NO(HZ)COMPONENTCOMPONENT(DEG)PHASE(DEG)
12.000E+042.046E+021.000E+009.000E+010.000E+00
24.000E+041.219E+025.956E-01-9.000E+01-2.700E+02
36.000E+042.852E+011.394E-019.000E+01-1.800E+02
48.000E+043.556E+011.738E-019.000E+01-2.700E+02
51.000E+055.108E+012.496E-01-9.000E+01-5.400E+02
61.200E+052.698E+011.319E-019.000E+01-4.500E+02
71.400E+059.030E+004.413E-029.000E+01-5.400E+02
81.600E+052.976E+011.454E-01-9.000E+01-8.100E+02
91.800E+052.452E+011.198E-019.000E+01-7.200E+02
102.000E+052.411E+001.178E-02-9.000E+01-9.900E+02
112.200E+051.758E+018.589E-02-9.000E+01-1.080E+03
122.400E+052.128E+011.040E-019.000E+01-9.900E+02
132.600E+058.492E+004.150E-02-9.000E+01-1.260E+03
142.800E+058.964E+004.380E-02-9.000E+01-1.350E+03
153.000E+051.744E+018.520E-029.000E+01-1.260E+03
163.200E+051.164E+015.688E-02-9.000E+01-1.530E+03
173.400E+052.432E+001.188E-02-9.000E+01-1.620E+03
183.600E+051.321E+016.457E-029.000E+01-1.530E+03
193.800E+051.279E+016.252E-02-9.000E+01-1.800E+03
204.000E+052.522E+001.232E-029.000E+01-1.710E+03
214.200E+058.851E+004.325E-029.000E+01-1.800E+03
224.400E+051.246E+016.087E-02-9.000E+01-2.070E+03
234.600E+056.092E+002.977E-029.000E+01-1.980E+03
TOTALHARMONICDISTORTION=7.541966E+01PERCENT
JOBCONCLUDED
TOTALJOBTIME.83
(1),Thetheaveragevalueinvois7.940968E+01,thatis79.40968v,andtheharmoniccomponents
invoislistedinthethirdlineonthetable.
(2),thermsvalueoftherippleinvo
V0=vd*√(1-(2*D-1)^2)=200*√(1-(2*0.708-1)^2)=181.873v
4,BymeansofFourieranalysis,calculatetheaveragevalueofidandthermsvalueofthe
Ripple.
FOURIERCOMPONENTSOFTRANSIENTRESPONSEI(V_V1)
DCCOMPONENT=-2.794380E+00
HARMONICFREQUENCYFOURIERNORMALIZEDPHASENORMALIZED
NO(HZ)COMPONENTCOMPONENT(DEG)PHASE(DEG)
12.000E+047.057E+001.000E+00-9.508E+010.000E+00
24.000E+044.204E+005.957E-019.552E+012.857E+02
36.000E+041.136E+001.609E-01-5.961E+012.256E+02
48.000E+041.273E+001.804E-01-1.062E+022.741E+02
51.000E+051.753E+002.485E-019.032E+015.657E+02
61.200E+059.572E-011.356E-01-7.561E+014.949E+02
71.400E+053.979E-015.638E-02-1.286E+025.369E+02
81.600E+051.024E+001.451E-018.581E+018.464E+02
91.800E+058.495E-011.204E-01-8.273E+017.730E+02
102.000E+052.002E-012.837E-021.558E+021.107E+03
112.200E+056.121E-018.673E-028.011E+011.126E+03
122.400E+057.320E-011.037E-01-8.744E+011.053E+03
132.600E+053.189E-014.518E-021.141E+021.350E+03
142.800E+053.273E-014.637E-026.985E+011.401E+03
153.000E+055.996E-018.496E-02-9.153E+011.335E+03
163.200E+054.081E-015.783E-021.021E+021.623E+03
173.400E+051.355E-011.920E-023.773E+011.654E+03
183.600E+054.569E-016.474E-02-9.601E+011.615E+03
193.800E+054.411E-016.250E-029.593E+011.902E+03
204.000E+051.273E-011.805E-02-4.322E+011.858E+03
214.200E+053.118E-014.418E-02-1.024E+021.894E+03
224.400E+054.272E-016.054E-029.152E+012.183E+03
234.600E+052.220E-013.146E-02-7.089E+012.116E+03
TOTALHARMONICDISTORTION=7.625045E+01PERCENT
theaveragevalueofidis-2.794380E+00(DCCOMPONENT),thatis-2.794380A,%THD=Ish/Is1*100%,soIsh=5.38A,thermsvalueoftheRippleis√(Is1^2+∑Ish^2)=6.275A
5,WithVEMF=0andIa(avg)=0,Vo(avg)=0V.Therefore,Vcontrol=0.Calculate
thefollowing[Hint:
useIo(0)=-1.67A]:
(a)vo,ioandpo(t)waveforms.
(b)peak-to-peakrippleinio.Compareitwithitsanalyticalvalue,andthatin
Problem2.
(c)Inpart(a),labeltheintervalsduringwhichvariousdevicesareconducting
Answer:
(a)vowaveform:
Iowaveform:
Powaveform:
(b)peak-to-peakrippleinio.
FromIowaveform,wecanseethepeaktopeakrippleiniois(0.7197v-(-2.4581v))=3.178v
(C)
6,Intheregenerativemode,thepowerflowsfromtheloadtothedc-busatVd.Let
VEMF=79.5V,Ia(avg)=10Ainthereversedirection,andVo(avg)=79.5-0.37x10
=
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